Embedded positive constant r-mean curvature hypersurfaces in Mm × R

Author:

Cheng Xu1,Rosenberg Harold2

Affiliation:

1. Universidade Federal Fluminense, Brasil

2. Université Paris 7, France

Abstract

Let M be an m-dimensional Riemannian manifold with sectional curvature bounded from below. We consider hypersurfaces in the (m + 1)-dimensional product manifold M × R with positive constant r-mean curvature. We obtain height estimates of certain compact vertical graphs in M × R with boundary in M × {0}. We apply this to obtain topological obstructions for the existence of some hypersurfaces. We also discuss the rotational symmetry of some embedded complete surfaces in S² × R of positive constant 2-mean curvature.

Publisher

FapUNIFESP (SciELO)

Subject

Multidisciplinary

Reference9 articles.

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3. Stability of hypersurfaces with constant r-mean curvature;BARBOSA JL;Ann Global Anal Geom,1997

4. Constant positive 2-mean curvature hypersurfaces;ELBERT MF;Illinois. J Math,2002

5. Inequalities;HARDY G,1989

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