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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Optimal length estimates for stable CMC surfaces in $3$-space forms
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by Laurent Mazet PDF
Proc. Amer. Math. Soc. 137 (2009), 2761-2765 Request permission

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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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