The Weil-Petersson geodesic flow is ergodic

Abstract

We prove that the geodesic flow for the Weil-Petersson metric on the moduli space of Riemann surfaces is ergodic (and in fact Bernoulli) and has finite, positive metric entropy.

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      AUTHOR = {Wolpert, Scott A.},
      TITLE = {Geometry of the {W}eil-{P}etersson completion of {T}eichmüller space},
      BOOKTITLE = {Surveys in Differential Geometry, {V}ol. {VIII}},
      VENUE={{B}oston, {MA},
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      PUBLISHER = {Conference Board of the Mathematical Sciences, Washington, DC},
      YEAR = {2010},
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      ISBN = {978-0-8218-4986-6},
      MRCLASS = {32G15 (30F60)},
      MRNUMBER = {2641916},
      MRREVIEWER = {Lee-Peng Teo},
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      }
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      MRREVIEWER = {A. Morimoto},
      DOI = {10.1017/S0143385700002807},
      ZBLNUMBER = {0578.58033},
      }

Authors

Keith Burns

Department of Mathematics
Northwestern University
2033 Sheridan Road
Evanston, IL 60208-2730

Howard Masur

Department of Mathematics
University of Chicago
5734 S. University Avenue
Chicago, IL 60637

Amie Wilkinson

Department of Mathematics
University of Chicago
5734 S. University Avenue
Chicago, IL 60637