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Proceedings of the American Mathematical Society

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


Author: Laurent Mazet
Journal: Proc. Amer. Math. Soc. 137 (2009), 2761-2765
MSC (2000): Primary 53A10
DOI: https://doi.org/10.1090/S0002-9939-09-09885-2
Published electronically: March 18, 2009
MathSciNet review: 2497490
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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.


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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
Email: laurent.mazet@math.cnrs.fr

DOI: https://doi.org/10.1090/S0002-9939-09-09885-2
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
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.