Conformal Extentsion of Metrics of Negative Curvature

Details Conformal Extentsion of Metrics of Negative Curvature Conformal Extentsion of Metrics of Negative Curvature

2002-02-25

arxiv.org/abs/math/0202249v2

J. Anal. Math. 91 (2003), 193--209.

Mathematics

Differential Geometry

In Memory of Robert Brooks. An analysis of Gromov's example added. 20 pages, 5 figures. to appear in Journal d'Analyse Mathema

Scientific paper

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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