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Grafting hyperbolic metrics and Eisenstein series

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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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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Science, Kagoshima University, 21-35 Korimoto 1-Chome, Kagoshima, 890-0065, Japan

    Kunio Obitsu

  2. Department of Mathematics, University of Maryland, College Park, MD, 20742, USA

    Scott A. Wolpert

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  1. Kunio Obitsu
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  2. Scott A. Wolpert
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Correspondence to Kunio Obitsu.

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Obitsu, K., Wolpert, S.A. Grafting hyperbolic metrics and Eisenstein series. Math. Ann. 341, 685–706 (2008). https://doi.org/10.1007/s00208-008-0210-y

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  • DOI: https://doi.org/10.1007/s00208-008-0210-y

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