The Weil-Petersson geodesic flow is ergodic

TL;DR

This paper proves that the geodesic flow on the moduli space of Riemann surfaces, equipped with the Weil-Petersson metric, is ergodic, Bernoulli, and has finite positive metric entropy.

Contribution

It establishes the ergodic and Bernoulli nature of the Weil-Petersson geodesic flow, a significant result in the dynamics of moduli spaces.

Findings

Proves ergodicity of the Weil-Petersson geodesic flow

Shows the flow is Bernoulli

Demonstrates finite positive metric entropy

Abstract

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