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Equidistribution of horospheres on moduli spaces of hyperbolic surfaces
- Publication Year :
- 2019
-
Abstract
- Given a simple closed curve $\gamma$ on a connected, oriented, closed surface $S$ of negative Euler characteristic, Mirzakhani showed that the set of points in the moduli space of hyperbolic structures on $S$ having a simple closed geodesic of length $L$ of the same topological type as $\gamma$ equidistributes with respect to a natural probability measure as $L \to \infty$. We prove several generalizations of Mirzakhani's result and discuss some of the technical aspects ommited in her original work. The dynamics of the earthquake flow play a fundamental role in the arguments in this paper.<br />Comment: 41 pages
- Subjects :
- Mathematics - Dynamical Systems
Mathematics - Geometric Topology
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1912.03856
- Document Type :
- Working Paper