Conformal Extentsion of Metrics of Negative Curvature
Differential Geometry
2007-05-23 v2
Abstract
We consider the problem of extending a conformal metric of negative curvature, given outside a neighbourhood of 0 in the unit disk , to a conformal metric of negative curvature in . 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.
Keywords
Cite
@article{arxiv.math/0202249,
title = {Conformal Extentsion of Metrics of Negative Curvature},
author = {Dan Mangoubi},
journal= {arXiv preprint arXiv:math/0202249},
year = {2007}
}
Comments
In Memory of Robert Brooks. An analysis of Gromov's example added. 20 pages, 5 figures. to appear in Journal d'Analyse Mathematique