Spacelike graphs with parallel mean curvature
Abstract
Description
We consider spacelike graphs $Γ_f$ of simple products $(M\times N, g\times -h)$ where $(M,g)$ and $(N,h)$ are Riemannian manifolds and $f:M\to N$ is a smooth map. Under the condition of the Cheeger constant of $M$ to be zero and some condition on the second fundamental form at infinity, we conclude that if $Γ_f \subset M\times N$ has parallel mean curvature $H$ then $H=0$. This holds trivially if $M$ is closed. If $M$ is the $m$-hyperbolic space then for any constant $c$, we describe a explicit foliation of $H^m\times R$ by hypersurfaces with constant mean curvature $c$.
11 pages. Some small corrrections of version 1. To appear in the Bull. Belgian Math. Soc. Simon Stevin
11 pages. Some small corrrections of version 1. To appear in the Bull. Belgian Math. Soc. Simon Stevin