Nagoya Mathematical Journal

Topological uniqueness of negatively curved surfaces

Hsungrow Chan

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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.

Article information

Nagoya Math. J., Volume 199 (2010), 137-149.

First available in Project Euclid: 14 September 2010

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Zentralblatt MATH identifier

Primary: 0240G 0240M 0240E 0470B


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

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