### Abstract

We describe the proof that the geodesic flow for the Weil-Petersson metric on the moduli space of Riemann surfaces is ergodic and in fact Bernoulli. Other chapters in this volume complement this summary by describing in depth the needed implementation of the Hopf argument and some of the pertinent aspects of moduli spaces of Riemann surfaces (and Teichmüller theory).

Original language | English (US) |
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Title of host publication | Lecture Notes in Mathematics |

Publisher | Springer Verlag |

Pages | 157-174 |

Number of pages | 18 |

DOIs | |

State | Published - Jan 1 2017 |

### Publication series

Name | Lecture Notes in Mathematics |
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Volume | 2164 |

ISSN (Print) | 0075-8434 |

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Burns, K. H., Masur, H., & Wilkinson, A. (2017). Ergodicity of the weil–Petersson geodesic flow. In

*Lecture Notes in Mathematics*(pp. 157-174). (Lecture Notes in Mathematics; Vol. 2164). Springer Verlag. https://doi.org/10.1007/978-3-319-43059-1_4