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Transactions of the American Mathematical Society

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Constant mean curvature surfaces in $ M^2\times \mathbf{R}$


Authors: David Hoffman, Jorge H. S. de Lira and Harold Rosenberg
Journal: Trans. Amer. Math. Soc. 358 (2006), 491-507
MSC (2000): Primary 53C27, 58J60
DOI: https://doi.org/10.1090/S0002-9947-05-04084-5
Published electronically: September 26, 2005
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Abstract: The subject of this paper is properly embedded $ H-$surfaces in Riemannian three manifolds of the form $ M^2\times \mathbf{R}$, where $ M^2$ is a complete Riemannian surface. When $ M^2={\mathbf R}^2$, we are in the classical domain of $ H-$surfaces in $ {\mathbf R}^3$. In general, we will make some assumptions about $ M^2$ in order to prove stronger results, or to show the effects of curvature bounds in $ M^2$ on the behavior of $ H-$surfaces in $ M^2\times \mathbf{R}$.


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Additional Information

David Hoffman
Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305
Email: hoffman@math.stanford.edu

Jorge H. S. de Lira
Affiliation: Departamento de Matemática, Universidade Federal do Ceará, Fortaleza - Ceará - Brasil
Email: jherbert@mat.ufc.br

Harold Rosenberg
Affiliation: Institut de Mathematiques de Jussieu, Paris XIII, France
Email: rosen@math.jussieu.fr

DOI: https://doi.org/10.1090/S0002-9947-05-04084-5
Received by editor(s): December 1, 2003
Published electronically: September 26, 2005
Additional Notes: The first author was partially supported by research grant DE-FG03-95ER25250/A007 of the Applied Mathematical Science subprogram of the Office of Energy Research, U.S. Department of Energy, and National Science Foundation, Division of Mathematical Sciences research grant DMS-0139410.
The second author was partially supported by Cooperaçao Brasil-França - Ministère des Affaires ètrangères (France) and CAPES (Brasil)
Article copyright: © Copyright 2005 American Mathematical Society

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