Asymptotics of the Weil–Petersson Metric

Rafe Mazzeo, Jan Swoboda

Type: Article

Publication Date: 2016-06-03

Citations: 12

DOI: https://doi.org/10.1093/imrn/rnw056

Abstract

We consider the Riemann moduli space Mγ of conformal structures on a compact surface of genus γ>1 together with its Weil–Petersson metric gWP⁠. Our main result is that gWP admits a complete polyhomogeneous expansion in powers of the lengths of the short geodesics up to the singular divisors of the Deligne–Mumford compactification of Mγ⁠.

Locations

International Mathematics Research Notices - View
arXiv (Cornell University) - View - PDF

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