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Topological uniqueness of negatively curved surfaces

Published online by Cambridge University Press:  11 January 2016

Hsungrow Chan
Hsungrow Chan*
Affiliation:
National Pingtung University of Education, Pingtung 900-03, Taiwan, hchan@mail.npue.edu.tw
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Abstract

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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.

Keywords

0240G0240M0240E0470B
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 199 , September 2010 , pp. 137 - 149
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2010

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