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arXiv · 0704.3169

Grafting hyperbolic metrics and Eisenstein series

Kunio Obitsu·Scott A. Wolpert
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Abstract

The family hyperbolic metric for the plumbing variety $\{zw=t\}$ and the non holomorphic Eisenstein series $E(ζ;2)$ 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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Kunio Obitsu, Scott A. Wolpert. 2008-02-02. Grafting hyperbolic metrics and Eisenstein series. https://arxiv.org/abs/0704.3169

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