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September 2010 Topological uniqueness of negatively curved surfaces
Hsungrow Chan
Nagoya Math. J. 199: 137-149 (September 2010). DOI: 10.1215/00277630-2010-007

Abstract

In this paper we consider complete, noncompact, negatively curved surfaces that are twice continuously differentiably embedded in Euclidean three-space, showing that if such surfaces have square integrable second fundamental form, then their topology must, by the index method, be an annulus. We then show how this relates to some minimal surface theorems and has a corollary on minimal surfaces with finite total curvature. In addition, we discuss, by the index method, the relation between the topology and asymptotic curves. Finally, we apply the results yielded to the problem of isometrical immersions into Euclidean three-space of black hole models.

Citation

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Hsungrow Chan. "Topological uniqueness of negatively curved surfaces." Nagoya Math. J. 199 137 - 149, September 2010. https://doi.org/10.1215/00277630-2010-007

Information

Published: September 2010
First available in Project Euclid: 14 September 2010

zbMATH: 1201.53002
MathSciNet: MR2732335
Digital Object Identifier: 10.1215/00277630-2010-007

Subjects:
Primary: 0240E, 0240G, 0240M, 0470B

Rights: Copyright © 2010 Editorial Board, Nagoya Mathematical Journal

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Vol.199 • September 2010
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