The Weil-Petersson geodesic flow is ergodic

被引:22
作者
Burns, K. [1 ]
Masur, H. [2 ]
Wilkinson, A. [1 ]
机构
[1] Northwestern Univ, Evanston, IL 60208 USA
[2] Univ Chicago, Chicago, IL 60637 USA
基金
美国国家科学基金会;
关键词
EXTENSION; DIMENSION; SURFACES; SPACE;
D O I
10.4007/annals.2012.175.2.8
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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.
引用
收藏
页码:835 / 908
页数:74
相关论文
共 43 条
  • [1] [Anonymous], 1995, ENCY MATH APPL
  • [2] [Anonymous], 2008, Comparison theorems in Riemannian geometry
  • [3] [Anonymous], 1939, Ber. Verh. Sachs. Akad. Leipzig
  • [4] [Anonymous], 1988, CANADIAN MATH SOC SE
  • [5] Anosov DV., 1967, Trudy Mat. Inst. Steklov, V90, P1
  • [6] BALLMANN W, 1987, J DIFFER GEOM, V26, P337
  • [7] BALLMANN W, 1987, J DIFFER GEOM, V25, P249
  • [8] BALLMANN W, 1985, PROGR MATH, V61
  • [9] Hausdorff dimension and the Weil-Petersson extension to quasifuchsian space
    Bridgeman, Martin
    [J]. GEOMETRY & TOPOLOGY, 2010, 14 (02): : 799 - 831
  • [10] Bridson MR, 1999, GRUNDL MATH WISSEN, V319