An explicit upper bound for Weil-Petersson volumes of the moduli spaces of punctured Riemann surfaces

Samuel Grushevsky

doi:10.1007/PL00004496

An explicit upper bound for Weil-Petersson volumes of the moduli spaces of punctured Riemann surfaces

Samuel Grushevsky

Simons Center for Geometry & Physics

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

An explicit upper bound for the Weil-Petersson volumes of punctured Riemann surfaces is obtained using Penner's combinatorial integration scheme from [4]. It is shown that for a fixed number of punctures n and for genus g increasing, g→∞,^limn fixed ln vol_{W P}(script M signg,n)/g ln g ≤ 2, while this limit is exactly equal to two for n = 1.

Original language	English
Pages (from-to)	1-13
Number of pages	13
Journal	Mathematische Annalen
Volume	321
Issue number	1
DOIs	https://doi.org/10.1007/PL00004496
State	Published - 2001

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abstract = "An explicit upper bound for the Weil-Petersson volumes of punctured Riemann surfaces is obtained using Penner's combinatorial integration scheme from [4]. It is shown that for a fixed number of punctures n and for genus g increasing, g→∞,limn fixed ln volW P(script M signg,n)/g ln g ≤ 2, while this limit is exactly equal to two for n = 1.",

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AB - An explicit upper bound for the Weil-Petersson volumes of punctured Riemann surfaces is obtained using Penner's combinatorial integration scheme from [4]. It is shown that for a fixed number of punctures n and for genus g increasing, g→∞,limn fixed ln volW P(script M signg,n)/g ln g ≤ 2, while this limit is exactly equal to two for n = 1.

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An explicit upper bound for Weil-Petersson volumes of the moduli spaces of punctured Riemann surfaces

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