Illinois Journal of Mathematics

Minimal surfaces in ${\Bbb M}\sp 2\times\Bbb R$

Harold Rosenberg

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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.

Article information

Source
Illinois J. Math., Volume 46, Number 4 (2002), 1177-1195.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138473

Digital Object Identifier
doi:10.1215/ijm/1258138473

Mathematical Reviews number (MathSciNet)
MR1988257

Zentralblatt MATH identifier
1036.53008

Subjects
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 35J60: Nonlinear elliptic equations

Citation

Rosenberg, Harold. Minimal surfaces in ${\Bbb M}\sp 2\times\Bbb R$. Illinois J. Math. 46 (2002), no. 4, 1177--1195. doi:10.1215/ijm/1258138473. https://projecteuclid.org/euclid.ijm/1258138473


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