A general halfspace theorem for constant mean curvature surfaces
Differential Geometry
2011-02-21 v3
Abstract
In this paper, we prove a general halfspace theorem for constant mean curvature surfaces. Under certain hypotheses, we prove that, in an ambient space M^3, any constant mean curvature H_0 surface on one side of a constant mean curvature H_0 surface \Sigma_0 is an equidistant surface to \Sigma_0. The main hypotheses of the theorem are that \Sigma_0 is parabolic and the mean curvature of the equidistant surfaces to \Sigma_0 evolves in a certain way.
Cite
@article{arxiv.1007.2559,
title = {A general halfspace theorem for constant mean curvature surfaces},
author = {Laurent Mazet},
journal= {arXiv preprint arXiv:1007.2559},
year = {2011}
}
Comments
3 figures, sign mistakes at the beginning of Section 6 are corrected