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 Σ_0 is an equidistant surface to Σ_0. The main hypotheses of the theorem are that Σ_0 is parabolic and the mean curvature of the equidistant surfaces to Σ_0 evolves in a certain way.
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