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arXiv · 1007.2559

A general halfspace theorem for constant mean curvature surfaces

Laurent Mazet
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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.

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Laurent Mazet. 2010-07-15. A general halfspace theorem for constant mean curvature surfaces. https://arxiv.org/abs/1007.2559

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