English

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.

Keywords

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

R2 v1 2026-06-21T15:48:28.685Z