Spacelike Graphs with Parallel Mean Curvature
Salavessa, Isabel M.C.
Bull. Belg. Math. Soc. Simon Stevin, Tome 15 (2008) no. 1, p. 65-76 / Harvested from Project Euclid
We consider spacelike graphs $\Gamma_f$ of simple products $(M\times N, g\times -h)$ where $(M,g)$ and $(N,h)$ are Riemannian manifolds and $f:M\rightarrow N$ 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 $\Gamma_f\subset M\times N$ 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 an explicit foliation of $ {\mathbb H}^m\times \mathbb R$ by hypersurfaces with constant mean curvature $c$.
Publié le : 2008-02-15
Classification:  Parallel and Constant Mean curvature,  Lorentzian manifold,  space-like hypersurface,  isoperimetric inequality,  53C42,  53C50
@article{1203692447,
     author = {Salavessa, Isabel M.C.},
     title = {Spacelike Graphs with Parallel Mean Curvature},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {15},
     number = {1},
     year = {2008},
     pages = { 65-76},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1203692447}
}
Salavessa, Isabel M.C. Spacelike Graphs with Parallel Mean Curvature. Bull. Belg. Math. Soc. Simon Stevin, Tome 15 (2008) no. 1, pp.  65-76. http://gdmltest.u-ga.fr/item/1203692447/