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June 2013 Growth of Weil-Petersson Volumes and Random Hyperbolic Surface of Large Genus
Maryam Mirzakhani
J. Differential Geom. 94(2): 267-300 (June 2013). DOI: 10.4310/jdg/1367438650

Abstract

In this paper, we investigate the geometric properties of random hyperbolic surfaces of large genus. We describe the relationship between the behavior of lengths of simple closed geodesics on a hyperbolic surface and properties of the moduli space of such surfaces. First, we study the asymptotic behavior of Weil-Petersson volume $V^{g,n}$ of the moduli spaces of hyperbolic surfaces of genus $g$ with $n$ punctures as $g \to \infty$. Then we discuss basic geometric properties of a random hyperbolic surface of genus $g$ with respect to the Weil-Petersson measure as $g \to \infty$.

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Maryam Mirzakhani. "Growth of Weil-Petersson Volumes and Random Hyperbolic Surface of Large Genus." J. Differential Geom. 94 (2) 267 - 300, June 2013. https://doi.org/10.4310/jdg/1367438650

Information

Published: June 2013
First available in Project Euclid: 1 May 2013

zbMATH: 1270.30014
MathSciNet: MR3080483
Digital Object Identifier: 10.4310/jdg/1367438650

Rights: Copyright © 2013 Lehigh University

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Vol.94 • No. 2 • June 2013
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