A general halfspace theorem for constant mean curvature surfaces
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 M3, any constant mean curvature H0 surface on one side of a constant mean curvature H0 surface 0 is an equidistant surface to 0. The main hypotheses of the theorem are that 0 is parabolic and the mean curvature of the equidistant surfaces to 0 evolves in a certain way.
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