Grafting hyperbolic metrics and Eisenstein series
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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.
Published in Mathematischen Annalen, 2008. The original publication is available at http://www.springerlink.com
Published in Mathematischen Annalen, 2008. The original publication is available at http://www.springerlink.com