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Green's Functions for Quasi-Hyperbolic Metrics on Degenerating Riemann Surfaces with a Separating Node

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Abstract

In this article, we consider a family of compact Riemann surfaces of genus q ≥ 2 degenerating to a Riemann surface with a separating node and many non-separating nodes. We obtain the asymptotic behavior of Green's functions associated to a continuous family of quasi-hyperbolic metrics on such degenerating Riemann surfaces.

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore, 119260

    Wing-Keung To

  2. Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, 560, Japan

    Lin Weng

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  1. Wing-Keung To
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  2. Lin Weng
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To, WK., Weng, L. Green's Functions for Quasi-Hyperbolic Metrics on Degenerating Riemann Surfaces with a Separating Node. Annals of Global Analysis and Geometry 17, 239–265 (1999). https://doi.org/10.1023/A:1006506623667

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