Conformal Extentsion of Metrics of Negative Curvature

Dan Mangoubi

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Conformal Extentsion of Metrics of Negative Curvature

Dan Mangoubi

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Abstract

We consider the problem of extending a conformal metric of negative curvature, given outside a neighbourhood of 0 in the unit disk $\DD$, to a conformal metric of negative curvature in $\DD$. 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 apply these considerations to compactification of Riemann surfaces.

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BibTeX RIS

Dan Mangoubi. 2002-10-06. Conformal Extentsion of Metrics of Negative Curvature. https://arxiv.org/abs/math/0202249

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