A remark on Mirzakhani's asymptotic formulae
Kefeng Liu, Hao Xu
TL;DR
This paper addresses Mirzakhani's question on the asymptotic behavior of volume polynomials of moduli spaces and explores applications of her Weil-Petersson volume formulas.
Contribution
It provides an answer to Mirzakhani's question and demonstrates new applications of her asymptotic formulas for Weil-Petersson volumes.
Findings
Resolved the asymptotic behavior of the one-point volume polynomial.
Presented new applications of Mirzakhani's volume formulas.
Enhanced understanding of moduli space volume asymptotics.
Abstract
In this note, we answer a question of Mirzakhani on asymptotic behavior of the one-point volume polynomial of moduli spaces of curves. We also present some applications of Mirzakhani's asymptotic formulae of Weil-Petersson volumes.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Advanced Algebra and Geometry