Grafting hyperbolic metrics and Eisenstein series
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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