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.
The Weil-Petersson geodesic flow is ergodic
Pages 835-908 from Volume 175 (2012), Issue 2 by Keith Burns, Howard Masur, Amie Wilkinson
Keywords
Riccati equations, Weil-Petersson, ergodicity, geodesic flow, incomplete Riemannian manifolds, negative curvature, singular and nonuniform hyperbolicity MR
2993753
zbMATH
06025003
Milestones
Received: 12 August 2010Revised: 7 December 2010
Accepted: 8 April 2011
Published online: 1 March 2012
Full Article