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

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 x R with positive constant r-mean curvature. We obtain height estimates of certain compact vertical graphs in M x R with boundary in M x {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 x R of positive constant 2-mean curvature.

Keywords

• product manifold
• hypersurface
• r-mean curvature