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The behaviour of solutions of the Gaussian curvature equation near an isolated boundary point

Published online by Cambridge University Press:  01 November 2008

DANIELA KRAUS  and
OLIVER ROTH
DANIELA KRAUS
Affiliation:
Universität Würzburg, Mathematisches Institut, D–97074 Würzburg, Germany. e-mail: [email protected], [email protected]
OLIVER ROTH
Affiliation:
Universität Würzburg, Mathematisches Institut, D–97074 Würzburg, Germany. e-mail: [email protected], [email protected]
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Abstract

A classical result of Nitsche [22] about the behaviour of the solutions to the Liouville equation Δu = 4e2u near isolated singularities is generalized to solutions of the Gaussian curvature equation Δu = −κ(z)e2u where κ is a negative Hölder continuous function. As an application a higher–order version of the Yau–Ahlfors–Schwarz lemma for complete conformal Riemannian metrics is obtained.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 145 , Issue 3 , November 2008 , pp. 643 - 667
Copyright
Copyright © Cambridge Philosophical Society 2008

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