English

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 \DD\DD, to a conformal metric of negative curvature in \DD\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.

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