Abstract
We give the first part of a proof of Thurston’s Ending Lamination conjecture. In this part we show how to construct from the end invariants of a Kleinian surface group a “Lipschitz model” for the thick part of the corresponding hyperbolic manifold. This enables us to describe the topological structure of the thick part, and to give a priori geometric bounds.
-
[abikoff:survey] W. Abikoff, "Kleinian Groups—Geometrically Finite and Geometrically Perverse," in Geometry of Group Representations (Boulder, CO, 1987), Providence, RI: Amer. Math. Soc., 1988, pp. 1-50.
@incollection {abikoff:survey, MRKEY = {957510},
AUTHOR = {Abikoff, William},
TITLE = {Kleinian Groups---Geometrically Finite and Geometrically Perverse},
BOOKTITLE = {Geometry of Group Representations ({B}oulder, {\rm CO},
1987)},
SERIES = {Contemp. Math.},
NUMBER = {74},
PAGES = {1--50},
PUBLISHER = {Amer. Math. Soc.},
ADDRESS = {Providence, RI},
YEAR = {1988},
MRCLASS = {30F10 (30F40 32G15 57S30)},
MRNUMBER = {89j:30061},
MRREVIEWER = {V. V. Chueshev},
ZBLNUMBER = {0662.30043},
} -
[agol:tame] Agol, I., Tameness of hyperbolic 3-manifolds, preprint, 2004.
@unpublished{agol:tame,
author={Agol, I.},
TITLE={Tameness of hyperbolic 3-manifolds, preprint},
YEAR={2004},
NOTE={arXiv:math.GT/0405568},
} -
[ahlfors-bers]
L. Ahlfors and L. Bers, "Riemann’s mapping theorem for variable metrics," Ann. of Math., vol. 72, pp. 385-404, 1960.@article {ahlfors-bers, MRKEY = {0115006},
AUTHOR = {Ahlfors, Lars and Bers, Lipman},
TITLE = {Riemann's mapping theorem for variable metrics},
JOURNAL = {Ann. of Math.},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {72},
YEAR = {1960},
PAGES = {385--404},
ISSN = {0003-486X},
MRCLASS = {35.00 (30.00)},
MRNUMBER = {22 \#5813},
MRREVIEWER = {C. B. Morrey, Jr.},
DOI = {10.2307/1970141},
ZBLNUMBER = {0104.29902},
} -
[ahlfors:finitegen] L. V. Ahlfors, "Finitely generated Kleinian groups," Amer. J. Math., vol. 86, pp. 413-429, 1964.
@article {ahlfors:finitegen, MRKEY = {0167618},
AUTHOR = {Ahlfors, Lars V.},
TITLE = {Finitely generated {K}leinian groups},
JOURNAL = {Amer. J. Math.},
FJOURNAL = {American Journal of Mathematics},
VOLUME = {86},
YEAR = {1964},
PAGES = {413--429},
ISSN = {0002-9327},
MRCLASS = {30.49},
MRNUMBER = {29 \#4890},
MRREVIEWER = {M. H. Heins},
DOI = {10.2307/2373173},
ZBLNUMBER = {0133.04201},
} -
[short:notes] J. M. Alonso and et al., "Notes on word hyperbolic groups," in Group Theory from a Geometrical Viewpoint (Trieste, 1990), World Sci. Publ., River Edge, NJ, 1991, pp. 3-63.
@incollection {short:notes, MRKEY = {1170363},
AUTHOR = {Alonso, J. M. and et al.},
TITLE = {Notes on word hyperbolic groups},
BOOKTITLE = {Group Theory from a Geometrical Viewpoint ({T}rieste, 1990)},
PAGES = {3--63},
NOTE = {(H. Short, ed.)},
PUBLISHER = {World Sci. Publ., River Edge, NJ},
YEAR = {1991},
MRCLASS = {57M07 (20F38)},
MRNUMBER = {93g:57001},
ZBLNUMBER = {0849.20023},
} -
[anderson-canary:cores] J. W. Anderson and R. D. Canary, "Cores of hyperbolic $3$-manifolds and limits of Kleinian groups," Amer. J. Math., vol. 118, iss. 4, pp. 745-779, 1996.
@article {anderson-canary:cores, MRKEY = {1400058},
AUTHOR = {Anderson, James W. and Canary, Richard D.},
TITLE = {Cores of hyperbolic {$3$}-manifolds and limits of {K}leinian groups},
JOURNAL = {Amer. J. Math.},
FJOURNAL = {American Journal of Mathematics},
VOLUME = {118},
YEAR = {1996},
NUMBER = {4},
PAGES = {745--779},
ISSN = {0002-9327},
CODEN = {AJMAAN},
MRCLASS = {57N10 (30F40 57M50 57S30)},
MRNUMBER = {97k:57015},
MRREVIEWER = {Fr{é}d{é}ric Paulin},
URL = {http://muse.jhu.edu/journals/american_journal_of_mathematics/v118/118.4anderson.pdf},
ZBLNUMBER = {0863.30048},
} -
[benedetti-petronio] R. Benedetti and C. Petronio, Lectures on Hyperbolic Geometry, New York: Springer-Verlag, 1992.
@book {benedetti-petronio, MRKEY = {1219310},
AUTHOR = {Benedetti, Riccardo and Petronio, Carlo},
TITLE = {Lectures on Hyperbolic Geometry},
SERIES = {Universitext},
PUBLISHER = {Springer-Verlag},
ADDRESS = {New York},
YEAR = {1992},
PAGES = {xiv+330},
ISBN = {3-540-55534-X},
MRCLASS = {57M50 (30F40 30F60 51M10 57N10)},
MRNUMBER = {94e:57015},
MRREVIEWER = {Colin C. Adams},
ZBLNUMBER = {0768.51018},
} -
[bers:simultaneous] L. Bers, "Simultaneous uniformization," Bull. Amer. Math. Soc., vol. 66, pp. 94-97, 1960.
@article {bers:simultaneous, MRKEY = {0111834},
AUTHOR = {Bers, Lipman},
TITLE = {Simultaneous uniformization},
JOURNAL = {Bull. Amer. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical Society},
VOLUME = {66},
YEAR = {1960},
PAGES = {94--97},
ISSN = {0002-9904},
MRCLASS = {30.00},
MRNUMBER = {22 \#2694},
MRREVIEWER = {H. L. Royden},
DOI = {10.1090/S0002-9904-1960-10413-2},
ZBLNUMBER = {0090.05101},
} -
[bers:boundaries] L. Bers, "On boundaries of Teichmüller spaces and on Kleinian groups. I," Ann. of Math., vol. 91, pp. 570-600, 1970.
@article {bers:boundaries, MRKEY = {0297992},
AUTHOR = {Bers, Lipman},
TITLE = {On boundaries of {T}eichmüller spaces and on {K}leinian groups. {I}},
JOURNAL = {Ann. of Math.},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {91},
YEAR = {1970},
PAGES = {570--600},
ISSN = {0003-486X},
MRCLASS = {30A60},
MRNUMBER = {45 \#7044},
MRREVIEWER = {L. Keen},
ZBLNUMBER={0197.06001},
DOI = {10.2307/1970638},
} -
[bers:spaces] L. Bers, "Spaces of Kleinian groups," in Several Complex Variables, (Proc. Conf., Univ. Maryland, College Park, Md., 1970), New York: Springer-Verlag, 1970, p. lecture notes in math. 155, 9-34.
@incollection{bers:spaces,
author={Bers, Lipman},
TITLE={Spaces of {K}leinian groups},
BOOKTITLE={Several Complex Variables, ({P}roc. {C}onf., {U}niv. {M}aryland, {C}ollege {P}ark, {M}d., 1970)},
PAGES={{\it Lecture Notes in Math.} {\bf 155},
9--34},
PUBLISHER={Springer-Verlag},
ADDRESS={New York},
YEAR={1970} , MRNUMBER={0271333},
} -
[bers:degenerating] L. Bers, "Spaces of degenerating Riemann surfaces," in Discontinuous Groups and Riemann Surfaces (Proc. Conf., Univ. Maryland, College Park, Md., 1973), Princeton, NJ: Princeton Univ. Press, 1974, vol. 79, pp. 43-55.
@incollection {bers:degenerating, MRKEY = {0361051},
AUTHOR = {Bers, Lipman},
TITLE = {Spaces of degenerating {R}iemann surfaces},
BOOKTITLE = {Discontinuous Groups and {R}iemann Surfaces ({P}roc. {C}onf., {U}niv. {M}aryland, {C}ollege {P}ark, {M}d., 1973)},
PAGES = {43--55},
SERIES={Ann. of Math. Studies},
VOLUME={79},
PUBLISHER = {Princeton Univ. Press},
ADDRESS = {Princeton, NJ},
YEAR = {1974},
MRCLASS = {30A46},
MRNUMBER = {50 \#13497},
MRREVIEWER = {C. Earle},
ZBLNUMBER = {0294.32016},
} -
[bers:inequality] L. Bers, "An inequality for Riemann surfaces," in Differential Geometry and Complex Analysis, New York: Springer-Verlag, 1985, pp. 87-93.
@incollection{bers:inequality,
author={Bers, Lipman},
TITLE={An inequality for {R}iemann surfaces},
BOOKTITLE={Differential Geometry and Complex Analysis},
PUBLISHER={Springer-Verlag},
ADDRESS={New York},
YEAR={1985},
PAGES={87--93},
ZBLNUMBER ={0575.30039},
MRNUMBER={0780038}
} -
[bonahon] F. Bonahon, "Bouts des variétés hyperboliques de dimension $3$," Ann. of Math., vol. 124, iss. 1, pp. 71-158, 1986.
@article {bonahon, MRKEY = {847953},
AUTHOR = {Bonahon, Francis},
TITLE = {Bouts des variétés hyperboliques de dimension {$3$}},
JOURNAL = {Ann. of Math.},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {124},
YEAR = {1986},
NUMBER = {1},
PAGES = {71--158},
ISSN = {0003-486X},
CODEN = {ANMAAH},
MRCLASS = {57N10 (30F40 32G15)},
MRNUMBER = {88c:57013},
MRREVIEWER = {G. Peter Scott},
DOI = {10.2307/1971388},
ZBLNUMBER = {0671.57008},
} -
[bonahon:laminations] F. Bonahon, "Geodesic laminations on surfaces," in Laminations and Foliations in Dynamics, Geometry and Topology (Stony Brook, NY, 1998), Providence, RI: Amer. Math. Soc., 2001, vol. 269, pp. 1-37.
@incollection {bonahon:laminations, MRKEY = {1810534},
AUTHOR = {Bonahon, Francis},
TITLE = {Geodesic laminations on surfaces},
BOOKTITLE = {Laminations and Foliations in Dynamics, Geometry and Topology ({S}tony {B}rook, {\rm NY},
1998)},
SERIES = {Contemp. Math.},
VOLUME = {269},
PAGES = {1--37},
PUBLISHER = {Amer. Math. Soc.},
ADDRESS = {Providence, RI},
YEAR = {2001},
MRCLASS = {57M50 (37C85 57N05 57R30)},
MRNUMBER = {2001m:57023},
MRREVIEWER = {Thierry Barbot},
ZBLNUMBER = {0996.53029},
} -
[bowditch:hyperbolicity] B. H. Bowditch, "Notes on Gromov’s hyperbolicity criterion for path-metric spaces," in Group Theory from a Geometrical Viewpoint (Trieste, 1990), World Sci. Publ., River Edge, NJ, 1991, pp. 64-167.
@incollection {bowditch:hyperbolicity, MRKEY = {1170364},
AUTHOR = {Bowditch, B. H.},
TITLE = {Notes on {G}romov's hyperbolicity criterion for path-metric spaces},
BOOKTITLE = {Group Theory from a Geometrical Viewpoint ({T}rieste, 1990)},
PAGES = {64--167},
PUBLISHER = {World Sci. Publ., River Edge, NJ},
YEAR = {1991},
MRCLASS = {57M07 (53C23)},
MRNUMBER = {93h:57002},
MRREVIEWER = {Tadeusz Januszkiewicz},
ZBLNUMBER = {0843.20031},
} -
[bowditch:elcgen] Bowditch, B. H., End invariants of hyperbolic 3-manifolds, 2005.
@unpublished{bowditch:elcgen,
author={Bowditch, B. H.},
TITLE={End invariants of hyperbolic 3-manifolds},
YEAR={2005},
NOTE={preprint},
}\marginpar{Checked} -
[brock:continuity] J. F. Brock, "Continuity of Thurston’s length function," Geom. Funct. Anal., vol. 10, iss. 4, pp. 741-797, 2000.
@article {brock:continuity, MRKEY = {1791139},
AUTHOR = {Brock, J. F.},
TITLE = {Continuity of {T}hurston's length function},
JOURNAL = {Geom. Funct. Anal.},
FJOURNAL = {Geometric and Functional Analysis},
VOLUME = {10},
YEAR = {2000},
NUMBER = {4},
PAGES = {741--797},
ISSN = {1016-443X},
CODEN = {GFANFB},
MRCLASS = {57M50 (57M27 57N10 57R30)},
MRNUMBER = {2001g:57028},
MRREVIEWER = {Sandra L. Shields},
DOI = {10.1007/PL00001637},
ZBLNUMBER = {0968.57011},
} -
[brock-canary-minsky:ELCII] Brooks, Robert and Canary, Richard D and Minsky, Yair N., The classification of Kleinian surface groups II: the ending lamination conjecture, preprint.
@unpublished{brock-canary-minsky:ELCII,
author={Brooks, Robert and Canary, Richard D and Minsky, Yair N.},
TITLE={The classification of {Kleinian} surface groups {II}: the ending lamination conjecture, preprint},
NOTE={arXiv:math.GT/0412006},
} \marginpar{Check} -
[brooks-matelski] R. Brooks and P. J. Matelski, "Collars in Kleinian groups," Duke Math. J., vol. 49, iss. 1, pp. 163-182, 1982.
@article {brooks-matelski, MRKEY = {650375},
AUTHOR = {Brooks, Robert and Matelski, J. Peter},
TITLE = {Collars in {K}leinian groups},
JOURNAL = {Duke Math. J.},
FJOURNAL = {Duke Mathematical Journal},
VOLUME = {49},
YEAR = {1982},
NUMBER = {1},
PAGES = {163--182},
ISSN = {0012-7094},
CODEN = {DUMJAO},
MRCLASS = {30F40 (53A35)},
MRNUMBER = {83f:30039},
MRREVIEWER = {Troels Jørgensen},
URL = {http://projecteuclid.org/getRecord?id=euclid.dmj/1077315078},
ZBLNUMBER = {0484.30029},
} -
[buser:surfaces] P. Buser, Geometry and Spectra of Compact Riemann Surfaces, Boston, MA: Birkhäuser, 1992.
@book {buser:surfaces, MRKEY = {1183224},
AUTHOR = {Buser, Peter},
TITLE = {Geometry and Spectra of Compact {R}iemann Surfaces},
SERIES = {Progr. Math.},
NUMBER = {106},
PUBLISHER = {Birkhäuser},
ADDRESS = {Boston, MA},
YEAR = {1992},
PAGES = {xiv+454},
ISBN = {0-8176-3406-1},
MRCLASS = {58G25 (30F99)},
MRNUMBER = {93g:58149},
MRREVIEWER = {Robert Brooks},
ZBLNUMBER = {0770.53001},
} -
[calegari-gabai:tame] D. Calegari and D. Gabai, "Shrinkwrapping and the taming of hyperbolic 3-manifolds," J. Amer. Math. Soc., vol. 19, iss. 2, pp. 385-446, 2006.
@article {calegari-gabai:tame, MRKEY = {2188131},
AUTHOR = {Calegari, Danny and Gabai, David},
TITLE = {Shrinkwrapping and the taming of hyperbolic 3-manifolds},
JOURNAL = {J. Amer. Math. Soc.},
FJOURNAL = {Journal of the American Mathematical Society},
VOLUME = {19},
YEAR = {2006},
NUMBER = {2},
PAGES = {385--446},
ISSN = {0894-0347},
MRCLASS = {57M50 (30F40 57N10)},
MRNUMBER = {2006g:57030},
MRREVIEWER = {Bruno Zimmermann},
DOI = {10.1090/S0894-0347-05-00513-8},
ZBLNUMBER = {1090.57010},
} -
[canary:ends] R. D. Canary, "Ends of hyperbolic $3$-manifolds," J. Amer. Math. Soc., vol. 6, iss. 1, pp. 1-35, 1993.
@article {canary:ends, MRKEY = {1166330},
AUTHOR = {Canary, Richard D.},
TITLE = {Ends of hyperbolic {$3$}-manifolds},
JOURNAL = {J. Amer. Math. Soc.},
FJOURNAL = {Journal of the American Mathematical Society},
VOLUME = {6},
YEAR = {1993},
NUMBER = {1},
PAGES = {1--35},
ISSN = {0894-0347},
MRCLASS = {57M50 (30F40)},
MRNUMBER = {93e:57019},
MRREVIEWER = {Colin C. Adams},
DOI = {10.2307/2152793},
ZBLNUMBER = {0810.57006},
} -
[ceg] R. D. Canary, D. B. A. Epstein, and P. Green, "Notes on notes of Thurston," in Analytical and Geometric Aspects of Hyperbolic Space (Coventry/Durham, 1984), Cambridge: Cambridge Univ. Press, 1987, pp. 3-92.
@incollection {ceg, MRKEY = {903850},
AUTHOR = {Canary, R. D. and Epstein, D. B. A. and Green, P.},
TITLE = {Notes on notes of {T}hurston},
BOOKTITLE = {Analytical and Geometric Aspects of Hyperbolic Space ({C}oventry/{D}urham, 1984)},
SERIES = {London Math. Soc. Lecture Note Ser.},
NUMBER = {111},
PAGES = {3--92},
PUBLISHER = {Cambridge Univ. Press},
ADDRESS = {Cambridge},
YEAR = {1987},
MRCLASS = {57N10 (32G15 32G99 54A20 57M99 58F17)},
MRNUMBER = {89e:57008},
MRREVIEWER = {William Dunbar},
ZBLNUMBER = {0612.57009},
} -
[cannon:negative] J. W. Cannon, "The theory of negatively curved spaces and groups," in Ergodic Theory, Symbolic Dynamics, and Hyperbolic Spaces (Trieste, 1989), New York: Oxford Univ. Press, 1991, pp. 315-369.
@incollection {cannon:negative, MRKEY = {1130181},
AUTHOR = {Cannon, James W.},
TITLE = {The theory of negatively curved spaces and groups},
BOOKTITLE = {Ergodic Theory, Symbolic Dynamics, and Hyperbolic Spaces ({T}rieste, 1989)},
SERIES = {Oxford Sci. Publ.},
PAGES = {315--369},
PUBLISHER = {Oxford Univ. Press},
ADDRESS = {New York},
YEAR = {1991},
MRCLASS = {57S30 (20F32 53C23 57M07)},
MRNUMBER = {1130181},
ZBLNUMBER = {0764.57002},
} -
[casson-bleiler] A. J. Casson and S. A. Bleiler, Automorphisms of Surfaces after Nielsen and Thurston, Cambridge: Cambridge Univ. Press, 1988.
@book {casson-bleiler, MRKEY = {964685},
AUTHOR = {Casson, Andrew J. and Bleiler, Steven A.},
TITLE = {Automorphisms of Surfaces after {N}ielsen and {T}hurston},
SERIES = {London Math. Soc. Stud. Texts},
NUMBER = {9},
PUBLISHER = {Cambridge Univ. Press},
ADDRESS = {Cambridge},
YEAR = {1988},
PAGES = {iv+105},
ISBN = {0-521-34203-1},
MRCLASS = {57N05 (32G15 57R30 58F15)},
MRNUMBER = {89k:57025},
MRREVIEWER = {William Dunbar},
ZBLNUMBER = {0649.57008},
} -
[epstein-marden] D. B. A. Epstein and A. Marden, "Convex hulls in hyperbolic space, a theorem of Sullivan, and measured pleated surfaces," in Analytical and Geometric Aspects of Hyperbolic Space (Coventry/Durham, 1984), Cambridge: Cambridge Univ. Press, 1987, pp. 113-253.
@incollection {epstein-marden, MRKEY = {903852},
AUTHOR = {Epstein, D. B. A. and Marden, A.},
TITLE = {Convex hulls in hyperbolic space, a theorem of {S}ullivan, and measured pleated surfaces},
BOOKTITLE = {Analytical and Geometric Aspects of Hyperbolic Space ({C}oventry/{D}urham, 1984)},
SERIES = {London Math. Soc. Lecture Note Ser.},
NUMBER = {111},
PAGES = {113--253},
PUBLISHER = {Cambridge Univ. Press},
ADDRESS = {Cambridge},
YEAR = {1987},
MRCLASS = {52A55 (32G15 57N10 57R25 58F17)},
MRNUMBER = {89c:52014},
MRREVIEWER = {William Dunbar},
ZBLNUMBER = {0612.57010},
} -
[ghys-harpe] E. Ghys and P. de la Harpe (rm eds.), Sur les Groupes Hyperboliques d’après Mikhael Gromov, Boston, MA: Birkhäuser, 1990.
@book {ghys-harpe, MRKEY = {1086648},
AUTHOR={Ghys, E. and de la Harpe ({\rm eds.}), P.},
TITLE = {Sur les Groupes Hyperboliques d'après {M}ikhael {G}romov},
SERIES = {Progr. Math.},
NUMBER = {83},
NOTE = {(Papers from the Swiss Seminar on Hyperbolic Groups held in Bern, 1988)},
PUBLISHER = {Birkhäuser},
ADDRESS = {Boston, MA},
YEAR = {1990},
PAGES = {xii+285},
ISBN = {0-8176-3508-4},
MRCLASS = {53C23 (20F32 57M05 57S30)},
MRNUMBER = {92f:53050},
MRREVIEWER = {Viktor Schroeder},
ZBLNUMBER={0731.20025},
} -
[gromov:hypgroups] G. Gromov, Essays in Group Theory, New York: Springer-Verlag, 1987.
@book {gromov:hypgroups,
author={Gromov, G.},
MRKEY = {919826},
TITLE = {Essays in Group Theory},
SERIES = {Math. Sci. Res. Inst. Publ.},
NUMBER = {8},
PUBLISHER = {Springer-Verlag},
NOTE={(S. M. Gersten, ed.)},
ADDRESS = {New York},
YEAR = {1987},
PAGES = {vi+342},
ISBN = {0-387-96618-8},
MRCLASS = {20-06 (20Fxx 57-06)},
MRNUMBER = {88e:20004},
ZBLNUMBER = {0547.00016},
} -
[harvey:boundary] W. J. Harvey, "Boundary structure of the modular group," in Riemann Surfaces and Related Topics: Proc. 1978 Stony Brook Conference (State Univ. New York, Stony Brook, NY, 1978), Princeton, N.J.: Princeton Univ. Press, 1981, pp. 245-251.
@incollection {harvey:boundary, MRKEY = {624817},
AUTHOR = {Harvey, W. J.},
TITLE = {Boundary structure of the modular group},
BOOKTITLE = {Riemann Surfaces and Related Topics: {P}roc. 1978 {S}tony {B}rook {C}onference ({S}tate {U}niv. {N}ew {Y}ork, {S}tony {B}rook, {\rm NY},
1978)},
SERIES = {Ann. of Math. Stud.},
NUMBER = {97},
PAGES = {245--251},
PUBLISHER = {Princeton Univ. Press},
ADDRESS = {Princeton, N.J.},
YEAR = {1981},
MRCLASS = {32G15 (57N05)},
MRNUMBER = {83d:32022},
MRREVIEWER = {B. Maskit},
ZBLNUMBER = {0461.30036},
} -
[hatcher-thurston] A. Hatcher and W. Thurston, "A presentation for the mapping class group of a closed orientable surface," Topology, vol. 19, iss. 3, pp. 221-237, 1980.
@article {hatcher-thurston, MRKEY = {579573},
AUTHOR = {Hatcher, A. and Thurston, W.},
TITLE = {A presentation for the mapping class group of a closed orientable surface},
JOURNAL = {Topology},
FJOURNAL = {Topology. An International Journal of Mathematics},
VOLUME = {19},
YEAR = {1980},
NUMBER = {3},
PAGES = {221--237},
ISSN = {0040-9383},
CODEN = {TPLGAF},
MRCLASS = {57N05},
MRNUMBER = {81k:57008},
MRREVIEWER = {Frank Quinn},
DOI = {10.1016/0040-9383(80)90009-9},
ZBLNUMBER = {0447.57005},
} -
[hersonsky:inequality] S. Hersonsky, "A generalization of the Shimizu-Leutbecher and J\o rgensen inequalities to Möbius transformations in ${\bf R}^N$," Proc. Amer. Math. Soc., vol. 121, iss. 1, pp. 209-215, 1994.
@article {hersonsky:inequality, MRKEY = {1182701},
AUTHOR = {Hersonsky, Sa'ar},
TITLE = {A generalization of the {S}himizu-{L}eutbecher and {J}\o rgensen inequalities to {M}öbius transformations in {${\bf R}\sp N$}},
JOURNAL = {Proc. Amer. Math. Soc.},
FJOURNAL = {Proceedings of the American Mathematical Society},
VOLUME = {121},
YEAR = {1994},
NUMBER = {1},
PAGES = {209--215},
ISSN = {0002-9939},
CODEN = {PAMYAR},
MRCLASS = {30F40},
MRNUMBER = {94m:30085},
ZBLNUMBER={0812.30017},
DOI = {10.2307/2160384},
} -
[jorgensen:inequality] T. Jørgensen, "On discrete groups of Möbius transformations," Amer. J. Math., vol. 98, iss. 3, pp. 739-749, 1976.
@article {jorgensen:inequality, MRKEY = {0427627},
AUTHOR = {Jørgensen, Troels},
TITLE = {On discrete groups of {M}öbius transformations},
JOURNAL = {Amer. J. Math.},
FJOURNAL = {American Journal of Mathematics},
VOLUME = {98},
YEAR = {1976},
NUMBER = {3},
PAGES = {739--749},
ISSN = {0002-9327},
MRCLASS = {30A58},
MRNUMBER = {55 \#658},
ZBLNUMBER={0336.30007},
MRREVIEWER = {V. Chuckrow},
DOI = {10.2307/2373814},
} -
[kazhdan-margulis] D. A. Kazhdan and G. A. Margulis, "A proof of Selberg’s conjecture," Math. USSR Sb., vol. 4, pp. 147-152, 1968.
@article{kazhdan-margulis, TITLE={A proof of Selberg's conjecture},
AUTHOR={Kazhdan, D. A. and Margulis, G. A.},
JOURNAL={Math. {\rm USSR} Sb.},
VOLUME={4},
YEAR={1968},
PAGES={147--152},
MRNUMBER={0223487},
ZBLNUMBER={0241.22024},
} -
[klarreichcolonboundary] Klarreich, E., The boundary at infinity of the curve complex and the relative Teichmüller space, preprint.
@unpublished{klarreichcolonboundary,
author={Klarreich, E.},
TITLE={The boundary at infinity of the curve complex and the relative {Teichmüller} space, preprint},
NOTE={http://www.nasw.org/users/klarreich/research.htm},
} \marginpar{Check} -
[kra:spaces] I. Kra, "On spaces of Kleinian groups," Comment. Math. Helv., vol. 47, pp. 53-69, 1972.
@article {kra:spaces, MRKEY = {0306485},
AUTHOR = {Kra, Irwin},
TITLE = {On spaces of {K}leinian groups},
JOURNAL = {Comment. Math. Helv.},
FJOURNAL = {Commentarii Mathematici Helvetici},
VOLUME = {47},
YEAR = {1972},
PAGES = {53--69},
ISSN = {0010-2571},
MRCLASS = {30A58},
MRNUMBER = {46 \#5611},
MRREVIEWER = {C. Earle},
DOI = {10.1007/BF02566788},
ZBLNUMBER = {0239.30020},
} -
[kulkarni-shalen] R. S. Kulkarni and P. B. Shalen, "On Ahlfors’ finiteness theorem," Adv. Math., vol. 76, iss. 2, pp. 155-169, 1989.
@article {kulkarni-shalen, MRKEY = {1013665},
AUTHOR = {Kulkarni, Ravi S. and Shalen, Peter B.},
TITLE = {On {A}hlfors' finiteness theorem},
JOURNAL = {Adv. Math.},
FJOURNAL = {Advances in Mathematics},
VOLUME = {76},
YEAR = {1989},
NUMBER = {2},
PAGES = {155--169},
ISSN = {0001-8708},
CODEN = {ADMTA4},
MRCLASS = {57S30 (20H10 30F40 57N10)},
MRNUMBER = {91e:57067},
MRREVIEWER = {William Harvey},
ZBLNUMBER={0684.57019},
DOI = {10.1016/0001-8708(89)90046-7},
} -
[marden:geometry] A. Marden, "The geometry of finitely generated kleinian groups," Ann. of Math., vol. 99, pp. 383-462, 1974.
@article {marden:geometry, MRKEY = {0349992},
AUTHOR = {Marden, Albert},
TITLE = {The geometry of finitely generated kleinian groups},
JOURNAL = {Ann. of Math.},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {99},
YEAR = {1974},
PAGES = {383--462},
ISSN = {0003-486X},
MRCLASS = {30A58 (22E40)},
MRNUMBER = {50 \#2485},
MRREVIEWER = {C. Earle},
DOI = {10.2307/1971059},
ZBLNUMBER = {0282.30014},
} -
[marden-maskit] A. Marden and B. Maskit, "On the isomorphism theorem for Kleinian groups," Invent. Math., vol. 51, iss. 1, pp. 9-14, 1979.
@article {marden-maskit, MRKEY = {524274},
AUTHOR = {Marden, A. and Maskit, B.},
TITLE = {On the isomorphism theorem for {K}leinian groups},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {51},
YEAR = {1979},
NUMBER = {1},
PAGES = {9--14},
ISSN = {0020-9910},
CODEN = {INVMBH},
MRCLASS = {30F40 (57M99)},
MRNUMBER = {80f:30037},
MRREVIEWER = {C. Earle},
DOI = {10.1007/BF01389909},
ZBLNUMBER = {0399.30037},
} -
[maskit:self] B. Maskit, "Self-maps on Kleinian groups," Amer. J. Math., vol. 93, pp. 840-856, 1971.
@article {maskit:self, MRKEY = {0291453},
AUTHOR = {Maskit, Bernard},
TITLE = {Self-maps on {K}leinian groups},
JOURNAL = {Amer. J. Math.},
FJOURNAL = {American Journal of Mathematics},
VOLUME = {93},
YEAR = {1971},
PAGES = {840--856},
ISSN = {0002-9327},
MRCLASS = {30A58},
MRNUMBER = {45 \#544},
MRREVIEWER = {J. Lehner},
DOI = {10.2307/2373474},
ZBLNUMBER = {0227.32007},
} -
[maskit:book] B. Maskit, Kleinian Groups, New York: Springer-Verlag, 1988.
@book {maskit:book, MRKEY = {959135},
AUTHOR = {Maskit, Bernard},
TITLE = {Kleinian Groups},
SERIES = {Grundl. Math. Wissen.},
NUMBER = {287},
PUBLISHER = {Springer-Verlag},
ADDRESS = {New York},
YEAR = {1988},
PAGES = {xiv+326},
ISBN = {3-540-17746-9},
MRCLASS = {30F40 (20H10 22E40)},
MRNUMBER = {90a:30132},
MRREVIEWER = {William Abikoff},
ZBLNUMBER = {0627.30039},
} -
[masur-minsky:complex1] H. A. Masur and Y. N. Minsky, "Geometry of the complex of curves. I. Hyperbolicity," Invent. Math., vol. 138, iss. 1, pp. 103-149, 1999.
@article {masur-minsky:complex1, MRKEY = {1714338},
AUTHOR = {Masur, Howard A. and Minsky, Yair N.},
TITLE = {Geometry of the complex of curves. {I}. {H}yperbolicity},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {138},
YEAR = {1999},
NUMBER = {1},
PAGES = {103--149},
ISSN = {0020-9910},
CODEN = {INVMBH},
MRCLASS = {57M50 (20F67 30F60 32G15)},
MRNUMBER = {2000i:57027},
MRREVIEWER = {Darryl McCullough},
DOI = {10.1007/s002220050343},
ZBLNUMBER = {0941.32012},
} -
[mmcomplextwo] H. A. Masur and Y. N. Minsky, "Geometry of the complex of curves. II. Hierarchical structure," Geom. Funct. Anal., vol. 10, iss. 4, pp. 902-974, 2000.
@article {mmcomplextwo, MRKEY = {1791145},
AUTHOR = {Masur, H. A. and Minsky, Y. N.},
TITLE = {Geometry of the complex of curves. {II}. {H}ierarchical structure},
JOURNAL = {Geom. Funct. Anal.},
FJOURNAL = {Geometric and Functional Analysis},
VOLUME = {10},
YEAR = {2000},
NUMBER = {4},
PAGES = {902--974},
ISSN = {1016-443X},
CODEN = {GFANFB},
MRCLASS = {57M50 (30F60 32G15)},
MRNUMBER = {2001k:57020},
MRREVIEWER = {Darryl McCullough},
DOI = {10.1007/PL00001643},
ZBLNUMBER = {0972.32011},
} -
[mccullough:relative] D. McCullough, "Compact submanifolds of $3$-manifolds with boundary," Quart. J. Math. Oxford Ser., vol. 37, iss. 147, pp. 299-307, 1986.
@article {mccullough:relative, MRKEY = {854628},
AUTHOR = {McCullough, Darryl},
TITLE = {Compact submanifolds of {$3$}-manifolds with boundary},
JOURNAL = {Quart. J. Math. Oxford Ser.},
FJOURNAL = {The Quarterly Journal of Mathematics. Oxford. Second Series},
VOLUME = {37},
YEAR = {1986},
NUMBER = {147},
PAGES = {299--307},
ISSN = {0033-5606},
CODEN = {QJMAAT},
MRCLASS = {57N10},
MRNUMBER = {88d:57012},
MRREVIEWER = {Shmuel Weinberger},
ZBLNUMBER = {0628.57008},
} -
[meyerhoff:volumes] R. Meyerhoff, "A lower bound for the volume of hyperbolic $3$-manifolds," Canad. J. Math., vol. 39, iss. 5, pp. 1038-1056, 1987.
@article {meyerhoff:volumes, MRKEY = {918586},
AUTHOR = {Meyerhoff, Robert},
TITLE = {A lower bound for the volume of hyperbolic {$3$}-manifolds},
JOURNAL = {Canad. J. Math.},
FJOURNAL = {Canadian Journal of Mathematics. Journal Canadien de Mathématiques},
VOLUME = {39},
YEAR = {1987},
NUMBER = {5},
PAGES = {1038--1056},
ISSN = {0008-414X},
CODEN = {CJMAAB},
MRCLASS = {57S30 (22E40 53C20)},
MRNUMBER = {88k:57049},
MRREVIEWER = {Robert Brooks},
ZBLNUMBER = {0694.57005},
} -
[minsky:taniguchi] Y. N. Minsky, "A geometric approach to the complex of curves on a surface," in Topology and Teichmüller Spaces (Katinkulta, 1995), World Sci. Publ., River Edge, NJ, 1996, pp. 149-158.
@incollection {minsky:taniguchi, MRKEY = {1659683},
AUTHOR = {Minsky, Yair N.},
TITLE = {A geometric approach to the complex of curves on a surface},
BOOKTITLE = {Topology and {T}eichmüller Spaces ({K}atinkulta, 1995)},
PAGES = {149--158},
PUBLISHER = {World Sci. Publ., River Edge, NJ},
YEAR = {1996},
MRCLASS = {32G15 (57M50)},
MRNUMBER = {2000g:32016},
MRREVIEWER = {Yoichi Imayoshi},
ZBLNUMBER = {0937.30027},
} -
[minsky:torus] Y. N. Minsky, "The classification of punctured-torus groups," Ann. of Math., vol. 149, iss. 2, pp. 559-626, 1999.
@article {minsky:torus, MRKEY = {1689341},
AUTHOR = {Minsky, Yair N.},
TITLE = {The classification of punctured-torus groups},
JOURNAL = {Ann. of Math.},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {149},
YEAR = {1999},
NUMBER = {2},
PAGES = {559--626},
ISSN = {0003-486X},
CODEN = {ANMAAH},
MRCLASS = {30F40 (57M50)},
MRNUMBER = {2000f:30028},
MRREVIEWER = {Darryl McCullough},
DOI = {10.2307/120976},
ZBLNUMBER = {0939.30034},
} -
[minsky:kgcc] Y. N. Minsky, "Kleinian groups and the complex of curves," Geom. Topol., vol. 4, pp. 117-148, 2000.
@article {minsky:kgcc, MRKEY = {2182094},
AUTHOR = {Minsky, Yair N.},
TITLE = {Kleinian groups and the complex of curves},
JOURNAL = {Geom. Topol.},
FJOURNAL = {Geometry and Topology},
VOLUME = {4},
YEAR = {2000},
PAGES = {117--148},
ISSN = {1465-3060},
MRCLASS = {57M50 (30F40)},
MRNUMBER = {2006k:57051},
MRREVIEWER = {Ken-ichi Ohshika},
DOI = {10.2140/gt.2000.4.117},
ZBLNUMBER = {0953.30027},
} -
[minsky:boundgeom] Y. N. Minsky, "Bounded geometry for Kleinian groups," Invent. Math., vol. 146, iss. 1, pp. 143-192, 2001.
@article {minsky:boundgeom, MRKEY = {1859020},
AUTHOR = {Minsky, Yair N.},
TITLE = {Bounded geometry for {K}leinian groups},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {146},
YEAR = {2001},
NUMBER = {1},
PAGES = {143--192},
ISSN = {0020-9910},
CODEN = {INVMBH},
MRCLASS = {30F40 (30F60 32G15 37F30 57M50)},
MRNUMBER = {2004f:30032},
MRREVIEWER = {Michel Coornaert},
DOI = {10.1007/s002220100163},
ZBLNUMBER = {1061.37026},
} -
[minsky:warwick] Kleinian Groups and Hyperbolic 3-ManifoldsCambridge: Cambridge Univ. Press, 2003.
@proceedings {minsky:warwick, MRKEY = {2044542},
TITLE = {Kleinian Groups and Hyperbolic 3-Manifolds},
SERIES = {London Math. Soc. Lecture Note Ser.},
NUMBER = {299},
EDITOR = {Komori, Y. and Markovic, V. and Series, C.},
ADDRESS = {Cambridge},
PUBLISHER = {Cambridge Univ. Press},
YEAR = {2003},
PAGES = {viii+384},
ISBN = {0-521-54013-5},
MRCLASS = {57-06 (30-06 57M50 57N10)},
MRNUMBER = {2004j:57001},
ZBLNUMBER={1031.30002},
} -
[moore:planetop] R. L. Moore, "On the foundations of plane analysis situs," Trans. Amer. Math. Soc., vol. 17, iss. 2, pp. 131-164, 1916.
@article {moore:planetop, MRKEY = {1501033},
AUTHOR = {Moore, Robert L.},
TITLE = {On the foundations of plane analysis situs},
JOURNAL = {Trans. Amer. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical Society},
VOLUME = {17},
YEAR = {1916},
NUMBER = {2},
PAGES = {131--164},
ISSN = {0002-9947},
CODEN = {TAMTAM},
MRCLASS = {54A05},
MRNUMBER = {1501033},
DOI = {10.2307/1989029},
} -
[moore:collapse] R. L. Moore, "Concerning upper semi-continuous collections of continua," Trans. Amer. Math. Soc., vol. 27, iss. 4, pp. 416-428, 1925.
@article {moore:collapse, MRKEY = {1501320},
AUTHOR = {Moore, R. L.},
TITLE = {Concerning upper semi-continuous collections of continua},
JOURNAL = {Trans. Amer. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical Society},
VOLUME = {27},
YEAR = {1925},
NUMBER = {4},
PAGES = {416--428},
ISSN = {0002-9947},
CODEN = {TAMTAM},
MRCLASS = {54F15 (54B99)},
MRNUMBER = {1501320},
DOI = {10.2307/1989234},
} -
[mostow:hyperbolic] G. D. Mostow, "Quasi-conformal mappings in $n$-space and the rigidity of hyperbolic space forms," Inst. Hautes Études Sci. Publ. Math., iss. 34, pp. 53-104, 1968.
@article {mostow:hyperbolic, MRKEY = {0236383},
AUTHOR = {Mostow, G. D.},
TITLE = {Quasi-conformal mappings in {$n$}-space and the rigidity of hyperbolic space forms},
JOURNAL = {Inst. Hautes Études Sci. Publ. Math.},
FJOURNAL = {Institut des Hautes Études Scientifiques. Publications Mathématiques},
NUMBER = {34},
YEAR = {1968},
PAGES = {53--104},
ISSN = {0073-8301},
MRCLASS = {30.47},
MRNUMBER = {38 \#4679},
MRREVIEWER = {R. J. Cannon},
URL = {http://www.numdam.org/item?id=PMIHES_1968__34__53_0},
ZBLNUMBER = {0189.09402},
} -
[penner-harer] R. C. Penner and J. L. Harer, Combinatorics of Train Tracks, Princeton, NJ: Princeton Univ. Press, 1992.
@book {penner-harer, MRKEY = {1144770},
AUTHOR = {Penner, R. C. and Harer, J. L.},
TITLE = {Combinatorics of Train Tracks},
SERIES = {Annals of Math. Studies},
NUMBER = {125},
PUBLISHER = {Princeton Univ. Press},
ADDRESS = {Princeton, NJ},
YEAR = {1992},
PAGES = {xii+216},
ISBN = {0-691-08764-4; 0-691-02531-2},
MRCLASS = {57M99 (30F60 57N05 57R30)},
MRNUMBER = {94b:57018},
MRREVIEWER = {Y. Minsky},
ZBLNUMBER = {0765.57001},
} -
[prasad] G. Prasad, "Strong rigidity of ${\bf Q}$-rank $1$ lattices," Invent. Math., vol. 21, pp. 255-286, 1973.
@article {prasad, MRKEY = {0385005},
AUTHOR = {Prasad, Gopal},
TITLE = {Strong rigidity of {${\bf Q}$}-rank {$1$} lattices},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {21},
YEAR = {1973},
PAGES = {255--286},
ISSN = {0020-9910},
MRCLASS = {22E40 (53C35)},
MRNUMBER = {52 \#5875},
MRREVIEWER = {M. S. Raghunathan},
DOI = {10.1007/BF01418789},
ZBLNUMBER = {0264.22009},
} -
[rees:elc] M. Rees, The ending laminations theorem direct from Teichmüller geodesics, 2004.
@misc{rees:elc,
author={Rees, M.},
TITLE={The ending laminations theorem direct from {Teichmüller} geodesics},
ARXIV={math.GT/0404007},
YEAR={2004},
} -
[scott:core] G. P. Scott, "Compact submanifolds of $3$-manifolds," J. London Math. Soc., vol. 7, pp. 246-250, 1973.
@article {scott:core, MRKEY = {0326737},
AUTHOR = {Scott, G. P.},
TITLE = {Compact submanifolds of {$3$}-manifolds},
JOURNAL = {J. London Math. Soc.},
FJOURNAL = {Journal of the London Mathematical Society. Second Series},
VOLUME = {7},
YEAR = {1973},
PAGES = {246--250},
ISSN = {0024-6107},
MRCLASS = {57A10},
MRNUMBER = {48 \#5080},
MRREVIEWER = {C. D. Feustel},
DOI = {10.1112/jlms/s2-7.2.246},
ZBLNUMBER = {0266.57001},
} -
[soma:elc] Soma, T., Geometric approach to Ending Lamination Conjecture, 2008, \marginparCheck.
@unpublished{soma:elc,
author={Soma, T.},
TITLE={Geometric approach to Ending Lamination Conjecture},
NOTE={arXiv:0801.4236},
YEAR={2008},
} \marginpar{Check} -
[sullivan:rigidity] D. Sullivan, "On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions," in Riemann Surfaces and Related Topics: Proc. 1978 Stony Brook Conference (State Univ. New York, Stony Brook, NY, 1978), Princeton, NJ: Princeton Univ. Press, 1981, pp. 465-496.
@incollection {sullivan:rigidity, MRKEY = {624833},
AUTHOR = {Sullivan, Dennis},
TITLE = {On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions},
BOOKTITLE = {Riemann Surfaces and Related Topics: {P}roc. 1978 {S}tony {B}rook {C}onference ({S}tate {U}niv. {N}ew {Y}ork, {S}tony {B}rook, {\rm NY},
1978)},
SERIES = {Ann. of Math. Studies},
NUMBER = {97},
PAGES = {465--496},
PUBLISHER = {Princeton Univ. Press},
ADDRESS = {Princeton, NJ},
YEAR = {1981},
MRCLASS = {58F11 (22E40 30C60 53C30 57R99)},
MRNUMBER = {83f:58052},
MRREVIEWER = {M. Rees},
ZBLNUMBER = {0567.58015},
} -
[wpt:II] Thurston, William P., Hyperbolic structures on 3-manifolds, II: surface groups and manifolds which fiber over the circle, preprint.
@unpublished{wpt:II,
author={Thurston, William P.},
TITLE={Hyperbolic structures on 3-manifolds, {II}: surface groups and manifolds which fiber over the circle, preprint},
NOTE={arXiv:math.GT/9801045},
} -
[wpt:notes] Thurston, William P., The geometry and topology of 3-manifolds, 1982.
@unpublished{wpt:notes,
author={Thurston, William P.},
TITLE={The geometry and topology of 3-manifolds},
JOURNAL={Princeton University Lecture Notes},
NOTE={online at http://www.msri.org/publications /books/gt3m},
YEAR={1982},
} -
[wpt:bull] W. P. Thurston, "Three-dimensional manifolds, Kleinian groups and hyperbolic geometry," Bull. Amer. Math. Soc., vol. 6, iss. 3, pp. 357-381, 1982.
@article {wpt:bull, MRKEY = {648524},
AUTHOR = {Thurston, William P.},
TITLE = {Three-dimensional manifolds, {K}leinian groups and hyperbolic geometry},
JOURNAL = {Bull. Amer. Math. Soc.},
FJOURNAL = {American Mathematical Society. Bulletin. New Series},
VOLUME = {6},
YEAR = {1982},
NUMBER = {3},
PAGES = {357--381},
ISSN = {0273-0979},
CODEN = {BAMOAD},
MRCLASS = {57N10 (20H15 30F40 57M35 57M40 57S17)},
MRNUMBER = {83h:57019},
MRREVIEWER = {Klaus Johannson},
DOI = {10.1090/S0273-0979-1982-15003-0},
ZBLNUMBER = {0496.57005},
} -
[wpt:I] W. P. Thurston, "Hyperbolic structures on $3$-manifolds. I. Deformation of acylindrical manifolds," Ann. of Math., vol. 124, iss. 2, pp. 203-246, 1986.
@article {wpt:I, MRKEY = {855294},
AUTHOR = {Thurston, William P.},
TITLE = {Hyperbolic structures on {$3$}-manifolds. {I}. {D}eformation of acylindrical manifolds},
JOURNAL = {Ann. of Math.},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {124},
YEAR = {1986},
NUMBER = {2},
PAGES = {203--246},
ISSN = {0003-486X},
CODEN = {ANMAAH},
MRCLASS = {57N10},
MRNUMBER = {88g:57014},
MRREVIEWER = {G. Peter Scott},
DOI = {10.2307/1971277},
ZBLNUMBER = {0668.57015},
} -
[wpt:textbook] W. P. Thurston, Three-Dimensional Geometry and Topology. Vol. 1, Princeton, NJ: Princeton Univ. Press, 1997.
@book {wpt:textbook, MRKEY = {1435975},
AUTHOR = {Thurston, William P.},
TITLE = {Three-Dimensional Geometry and Topology. {V}ol. 1},
SERIES = {Princeton Math. Series},
NUMBER = {35},
NOTE = {(Silvio Levy, ed.)},
PUBLISHER = {Princeton Univ. Press},
ADDRESS = {Princeton, NJ},
YEAR = {1997},
PAGES = {x+311},
ISBN = {0-691-08304-5},
MRCLASS = {57M50 (53A35 57M25 57M60 57N10)},
MRNUMBER = {97m:57016},
MRREVIEWER = {Athanase Papadopoulos},
ZBLNUMBER = {0873.57001},
} -
[waterman:inequality] P. L. Waterman, "Möbius transformations in several dimensions," Adv. Math., vol. 101, iss. 1, pp. 87-113, 1993.
@article {waterman:inequality, MRKEY = {1239454},
AUTHOR = {Waterman, P. L.},
TITLE = {Möbius transformations in several dimensions},
JOURNAL = {Adv. Math.},
FJOURNAL = {Advances in Mathematics},
VOLUME = {101},
YEAR = {1993},
NUMBER = {1},
PAGES = {87--113},
ISSN = {0001-8708},
CODEN = {ADMTA4},
MRCLASS = {30F35 (51M10)},
MRNUMBER = {95h:30056},
ZBLNUMBER={0793.15019},
DOI = {10.1006/aima.1993.1043},
}
Full Article