The asymptotic behavior of Green's functions for quasi-hyperbolic metrics on degenerating Riemann surfaces

Wing Keung To, Lin Weng

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this article, we consider a family of compact Riemann surfaces of genus q ≥ 2 degenerating to a Riemann surface of genus q-1 with a non-separating node. We show that the Green's functions associated to a continuous family of quasi-hyperbolic metrics on such degenerating Riemann surfaces simply degenerate to that on the smooth part of the noded Riemann surface.

Original languageEnglish
Pages (from-to)465-480
Number of pages16
JournalManuscripta Mathematica
Volume93
Issue number4
Publication statusPublished - Aug 1997
Externally publishedYes

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Hyperbolic Metric
Riemann Surface
Green's function
Asymptotic Behavior
Genus
Vertex of a graph
Family

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

The asymptotic behavior of Green's functions for quasi-hyperbolic metrics on degenerating Riemann surfaces. / To, Wing Keung; Weng, Lin.

In: Manuscripta Mathematica, Vol. 93, No. 4, 08.1997, p. 465-480.

Research output: Contribution to journalArticle

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