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

Abstract

In this paper, we study stable constant mean curvature $H$ surfaces in ${\mathbb{R}}^3$. We prove that, in such a surface, the distance from a point to the boundary is less that $\pi /(2H)$. This upper-bound is optimal and is extended to stable constant mean curvature surfaces in space forms.

7 pages