Weil-Petersson volumes and cone surfaces

TL;DR

This paper introduces new recursion relations for Weil-Petersson volume polynomials of hyperbolic surfaces with boundary, advancing the understanding of their geometric structure and volume calculations.

Contribution

It provides novel recursion formulas linking volume polynomials, extending Mirzakhani's recursive approach to moduli space volumes.

Findings

Derived new recursion relations for volume polynomials

Enhanced computational methods for moduli space volumes

Deepened understanding of hyperbolic surface geometry

Abstract

The moduli spaces of hyperbolic surfaces of genus g with n geodesic boundary components are naturally symplectic manifolds. Mirzakhani proved that their volumes are polynomials in the lengths of the boundaries by computing the volumes recursively. In this paper we give new recursion relations between the volume polynomials.