A general halfspace theorem for constant mean curvature surfaces

2010/07/15 by Laurent Mazet, Mazet, Laurent · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities #math.DG

paper · pdf · doi:10.48550/arxiv.1007.2559

3 figures, sign mistakes at the beginning of Section 6 are corrected

openalex publication_date 2010/07/15 · arxiv created 2011/02/18 · arxiv updated 2011/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Σ₀ is an equidistant surface to Σ₀. The main hypotheses of the theorem are that Σ₀ is parabolic and the mean curvature of the equidistant surfaces to Σ₀ evolves in a certain way.

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• Cylindrically bounded constant mean curvature surfaces in ℍ²×ℝ

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