The Weil-Petersson geodesic flow is ergodic

Keith Burns; Howard Masur; Amie Wilkinson

doi:https://doi.org/10.4007/annals.2012.175.2.8

Pages 835-908 from Volume 175 (2012), Issue 2 by Keith Burns, Howard Masur, Amie Wilkinson

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.

Milestones

Received: 12 August 2010
Revised: 7 December 2010
Accepted: 8 April 2011
Published online: 1 March 2012

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