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Grafting hyperbolic metrics and Eisenstein series

Author： Obitsu Kunio

Publisher： Springer Publishing Company

ISSN： 0025-5831

Source： Mathematische Annalen, Vol.341, Iss.3, 2008-07, pp. : 685-706

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

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Abstract

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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