Optimal length estimates for stable CMC surfaces in 3-space forms

2008/09/26 by Laurent Mazet, Mazet, Laurent
Mathematics · #53A10 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #math.DG #msc:53A10

paper · pdf · doi:10.48550/arxiv.0809.4612

7 pages

arxiv created 2008/09/26 · openalex publication_date 2008/09/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study stable constant mean curvature H surfaces in \R³. We prove that, in such a surface, the distance from a point to the boundary is less that π/(2H). This upper-bound is optimal and is extended to stable constant mean curvature surfaces in space forms.

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