Grafting hyperbolic metrics and Eisenstein series

Details Grafting hyperbolic metrics and Eisenstein series Grafting hyperbolic metrics and Eisenstein series

2007-04-24

arxiv.org/abs/0704.3169v2

Mathematics

Complex Variables

Published in Mathematischen Annalen, 2008. The original publication is available at http://www.springerlink.com

Scientific paper

The family hyperbolic metric for the plumbing variety $\{zw=t\}$ and the non
holomorphic Eisenstein series $E(\zeta;2)$ are combined to provide an explicit
expansion for the hyperbolic metrics for degenerating families of Riemann
surfaces. Applications include an asymptotic expansion for the Weil-Petersson
metric and a local form of symplectic reduction.

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