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Winter 2002 Minimal surfaces in ${\Bbb M}\sp 2\times\Bbb R$
Harold Rosenberg
Illinois J. Math. 46(4): 1177-1195 (Winter 2002). DOI: 10.1215/ijm/1258138473

Abstract

We study the geometry and topology of properly embedded minimal surfaces in $M\times\mathbb{R}$, where $M$ is a Riemannian surface. When $M$ is a round sphere, we give examples of all genus and we prove such minimal surfaces have exactly two ends or equal $M\times\{t\}$, for some real $t$. When $M$ has non-negative curvature, we study the conformal type of minimal surfaces in $M\times\mathbb{R}$, and we prove half-space theorems. When $M$ is the hyperbolic plane, we obtain a Jenkins-Serrin type theorem.

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Harold Rosenberg. "Minimal surfaces in ${\Bbb M}\sp 2\times\Bbb R$." Illinois J. Math. 46 (4) 1177 - 1195, Winter 2002. https://doi.org/10.1215/ijm/1258138473

Information

Published: Winter 2002
First available in Project Euclid: 13 November 2009

zbMATH: 1036.53008
MathSciNet: MR1988257
Digital Object Identifier: 10.1215/ijm/1258138473

Subjects:
Primary: 53A10
Secondary: 35J60

Rights: Copyright © 2002 University of Illinois at Urbana-Champaign

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Vol.46 • No. 4 • Winter 2002
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