Conformal extension of metrics of negative curvature

Dan Mangoubi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We consider the problem of extending a conformal metric of negative curvature, given outside of a neighbourhood of 0 in the unit disk double struck D sign, to a conformal metric of negative curvature in double struck D sigh. We give conditions under which such an extension is possible and also give obstructions to such an extension. The methods we use are based on a maximum principle and the Ahlfors-Schwarz Lemma. We also give an example in which no extension is possible, even when the conformality condition is dropped. We apply these considerations to the compactification of Riemann surfaces.

Original languageAmerican English
Pages (from-to)193-209
Number of pages17
JournalJournal d'Analyse Mathematique
Volume91
DOIs
StatePublished - 2003
Externally publishedYes

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