Foliations of Hyperbolic Space by Constant Mean Curvature Hypersurfaces
Differential Geometry
2010-05-03 v2 Geometric Topology
Abstract
We show that the constant mean curvature hypersurfaces in the hyperbolic n-space spanning the boundary of a star shaped C^{1,1} domain in the asymptotic sphere give a foliation of the hyperbolic n-space. We also show that if C is a closed codimension-1 C^{2,a} submanifold in the asymptotic sphere bounding a unique constant mean curvature hypersurface S_H in the hyperbolic n-space with asymptotic boundary C for any -1<H<1, then the constant mean curvature hypersurfaces {S_H} foliates the hyperbolic n-space.
Keywords
Cite
@article{arxiv.0909.5601,
title = {Foliations of Hyperbolic Space by Constant Mean Curvature Hypersurfaces},
author = {Baris Coskunuzer},
journal= {arXiv preprint arXiv:0909.5601},
year = {2010}
}