Abstract
This article considers the existence and regularity of Kähler–Einstein metrics on a compact Kähler manifold $M$ with edge singularities with cone angle $2\pi \beta$ along a smooth divisor $D$. We prove existence of such metrics with negative, zero and some positive cases for all cone angles $2\pi \beta \leq 2\pi$. The results in the positive case parallel those in the smooth case. We also establish that solutions of this problem are polyhomogeneous, i.e., have a complete asymptotic expansion with smooth coefficients along $D$ for all $2\pi \beta < 2\pi$.
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@article{Wu, mrkey = {2425471},
author = {Wu, Damin},
title = {Kähler-{E}instein metrics of negative {R}icci curvature on general quasi-projective manifolds},
journal = {Comm. Anal. Geom.},
fjournal = {Communications in Analysis and Geometry},
volume = {16},
year = {2008},
number = {2},
pages = {395--435},
issn = {1019-8385},
mrclass = {32Q20 (32W20 53C25)},
mrnumber = {2425471},
mrreviewer = {Julien Keller},
doi = {10.4310/CAG.2008.v16.n2.a4},
zblnumber = {1151.32009},
} -
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@article{Y1, mrkey = {0486659},
author = {Yau, Shing Tung},
title = {A general {S}chwarz lemma for {K}ähler manifolds},
journal = {Amer. J. Math.},
fjournal = {American Journal of Mathematics},
volume = {100},
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number = {1},
pages = {197--203},
issn = {0002-9327},
mrclass = {32H25 (53C55)},
mrnumber = {0486659},
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@article{Y2, mrkey = {0480350},
author = {Yau, Shing Tung},
title = {On the {R}icci curvature of a compact {K}ähler manifold and the complex {M}onge-{A}mpère equation. {I}},
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fjournal = {Communications on Pure and Applied Mathematics},
volume = {31},
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issn = {0010-3640},
coden = {CPAMAT},
mrclass = {53C55 (32C10 35J60)},
mrnumber = {0480350},
mrreviewer = {Robert E. Greene},
doi = {10.1002/cpa.3160310304},
zblnumber = {0369.53059},
}