Conformal Extentsion of Metrics of Negative Curvature
Abstract
Description
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.
In Memory of Robert Brooks. An analysis of Gromov's example added. 20 pages, 5 figures. to appear in Journal d'Analyse Mathematique
In Memory of Robert Brooks. An analysis of Gromov's example added. 20 pages, 5 figures. to appear in Journal d'Analyse Mathematique