Minimal surfaces in ${\Bbb M}\sp 2\times\Bbb R$
Rosenberg, Harold
Illinois J. Math., Tome 46 (2002) no. 3, p. 1177-1195 / Harvested from Project Euclid
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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.
Publié le : 2002-10-15
Classification:  53A10,  35J60 
@article{1258138473,
     author = {Rosenberg, Harold},
     title = {Minimal surfaces in ${\Bbb M}\sp 2\times\Bbb R$},
     journal = {Illinois J. Math.},
     volume = {46},
     number = {3},
     year = {2002},
     pages = { 1177-1195},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138473}
}

Rosenberg, Harold. Minimal surfaces in ${\Bbb M}\sp 2\times\Bbb R$. Illinois J. Math., Tome 46 (2002) no. 3, pp.  1177-1195. http://gdmltest.u-ga.fr/item/1258138473/