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

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## 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 than or equal to $\pi /(2H)$. This upper bound is optimal and is extended to stable constant mean curvature surfaces in space forms.## References

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## Additional Information

**Laurent Mazet**- Affiliation: Laboratoire d’Analyse et Mathématiques Appliquées, Université Paris-Est, CNRS UMR8050, UFR des Sciences et Technologie, Bâtiment P3 4eme étage, 61 avenue du Général de Gaulle, 94010 Créteil cedex, France
- MR Author ID: 722767
- Email: laurent.mazet@math.cnrs.fr
- Received by editor(s): September 26, 2008
- Received by editor(s) in revised form: January 7, 2009
- Published electronically: March 18, 2009
- Communicated by: Richard A. Wentworth
- © Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**137**(2009), 2761-2765 - MSC (2000): Primary 53A10
- DOI: https://doi.org/10.1090/S0002-9939-09-09885-2
- MathSciNet review: 2497490