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15 January 2012 Growth of the Weil–Petersson diameter of moduli space
William Cavendish, Hugo Parlier
Duke Math. J. 161(1): 139-171 (15 January 2012). DOI: 10.1215/00127094-1507312

Abstract

In this paper we study the Weil–Petersson geometry of g,n¯, the compactified moduli space of Riemann surfaces with genus g and n marked points. The main goal of this paper is to understand the growth of the diameter of g,n¯ as a function of g and n. We show that this diameter grows as n in n, and is bounded above by Cglogg in g for some constant C. We also give a lower bound on the growth in g of the diameter of g,n¯ in terms of an auxiliary function that measures the extent to which the thick part of moduli space admits radial coordinates.

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William Cavendish. Hugo Parlier. "Growth of the Weil–Petersson diameter of moduli space." Duke Math. J. 161 (1) 139 - 171, 15 January 2012. https://doi.org/10.1215/00127094-1507312

Information

Published: 15 January 2012
First available in Project Euclid: 30 December 2011

zbMATH: 1244.32008
MathSciNet: MR2872556
Digital Object Identifier: 10.1215/00127094-1507312

Subjects:
Primary: 32G15
Secondary: 30FXX

Rights: Copyright © 2012 Duke University Press

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Vol.161 • No. 1 • 15 January 2012
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