The asymptotic behavior of Green's functions for quasi-hyperbolic metrics on degenerating Riemann surfaces
type: Item
instance of: scholarly article
title: The asymptotic behavior of Green's functions for quasi-hyperbolic metrics on degenerating Riemann surfaces
zbMATH Open document ID: 0876.30045
DOI: 10.1007/BF02677486
author: Wing-Keung To
author: Lin Weng
published in: Manuscripta Mathematica
publication date: 1997-08-28T00:00:00Z
full work available at URL: https://eudml.org/doc/156314
review text: Let \(N\) be a punctured Riemann surface and \(ds^2\) a Hermitian metric on \(N\) which is of moderate growth near the punctures. Then there exists a unique Green's function for \(N\) with respect to \(ds^2\) satisfying the standard conditions and a suitable growth condition near the punctures (Theorem 1). The main aim of the paper under review is to study the behaviour of the Green's function for a family of compact Riemann surfaces of genus \(g\geq 2\) degenerating to a Riemann surface of genus \(g-1\) with a non-separating node. The authors show that the Green's functions associated to such a continuous family of so-called quasi-hyperbolic matrics simply degenerate to that on the smooth part of the noded surface (Theorem 2).
Mathematics Subject Classification ID: 30F45
Mathematics Subject Classification ID: 32G07
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 14H55
zbMATH DE Number: 1054316
zbMATH Keywords: Riemann surface
zbMATH Keywords: degeneration
zbMATH Keywords: Green's function
reviewed by: Jürgen Elstrodt
MaRDI profile type: Publication
cites work: Theta functions on Riemann surfaces
cites work: Elliptic Partial Differential Equations of Second Order
cites work: The asymptotic behavior of Green's functions for degenerating hyperbolic surfaces
cites work: Spectral degeneration of hyperboloc Riemann surfaces
cites work: Asymptotic behavior of Faltings's delta function
cites work: Q3994900
cites work: Q3891469
cites work: The asymptotics of the Arakelov-Green's function and Faltings' delta invariant
cites work: Asymptotics of the spectrum and the Selberg zeta function on the space of Riemann surfaces
cites work: The hyperbolic metric and the geometry of the universal curve
cites work: A General Schwarz Lemma for Kahler Manifolds
OpenAlex ID: W2031142319
description: scientific article; zbMATH DE number 1054316