Geometriae Dedicata

, 141:93

Weil–Petersson volumes and cone surfaces

Original Paper

DOI: 10.1007/s10711-008-9345-y

Cite this article as:
Do, N. & Norbury, P. Geom Dedicata (2009) 141: 93. doi:10.1007/s10711-008-9345-y


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.


Moduli space Hyperbolic surface Intersection number 

Mathematics Subject Classification (2000)

32G15 58D27 30F60 

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of MelbourneMelbourneAustralia