The asymptotic behavior of Green's functions for degenerating hyperbolic surfaces
type: Item
instance of: scholarly article
title: The asymptotic behavior of Green's functions for degenerating hyperbolic surfaces
zbMATH Open document ID: 0792.53040
DOI: 10.1007/BF02571664
author: Lizhen Ji
published in: Mathematische Zeitschrift
publication date: 1994-08-02T00:00:00Z
full work available at URL: https://eudml.org/doc/174493
review text: Let \(S_ l\) \((l\geq 0)\) be a degenerating family of hyperbolic surfaces. In particular, for \(l > 0\), \(S_ l\) is a compact surface with a metric of constant curvature \(-1\), but \(S_ 0\) is a complete and non-compact with a metric of constant curvature \(-1\) and of finite area. For each \(l \geq 0\), the Laplacian \(\Delta_ l\) of \(S_ l\) is invertible on the orthogonal complement of constant functions, and the Schwartz kernel of this inverse is called the Green function of \(S_ l\), and denoted by \(G(z,w;l)\) for \(z,w \in S_ l\). We get the asymptotic behavior of Green's function \(G(z,w;l)\) of \(S_ l\) as \(l\to 0\) in terms of the lengths of the pinching geodesics of the family \(S_ l\) and the topology of the limit surface.
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 58J37
zbMATH DE Number: 549762
zbMATH Keywords: constant curvature
zbMATH Keywords: Laplacian
zbMATH Keywords: Green function
zbMATH Keywords: pinching geodesics
MaRDI profile type: Publication
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OpenAlex ID: W1986771847
description: scientific article; zbMATH DE number 549762