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Optimal length estimates for stable CMC surfaces in  -space forms
Author(s):
Laurent
Mazet
Journal:
Proc. Amer. Math. Soc.
137
(2009),
2761-2765.
MSC (2000):
Primary 53A10
Posted:
March 18, 2009
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Abstract:
In this paper, we study stable constant mean curvature  surfaces in  . We prove that, in such a surface, the distance from a point to the boundary is less than or equal to  . This upper bound is optimal and is extended to stable constant mean curvature surfaces in space forms.
References:
-
- 1.
- Philippe Castillon.
An inverse spectral problem on surfaces.
Comment. Math. Helv., 81:271-286, 2006. MR 2225628 (2007b:58042) - 2.
- Tobias H. Colding and William P. Minicozzi II.
Estimates for parametric elliptic integrands.
Int. Math. Res. Not., 2002(6):291-297. MR 1877004 (2002k:53060) - 3.
- Jose M. Espinar and Harold Rosenberg.
A Colding-Minicozzi stability inequality and its applications,
to appear in Trans. Amer. Math. Soc. - 4.
- Doris Fischer-Colbrie and Richard Schoen.
The structure of complete stable minimal surfaces in  -manifolds of nonnegative scalar curvature.
Comm. Pure Appl. Math., 33:199-211, 1980. MR 562550 (81i:53044) - 5.
- H. Blaine Lawson, Jr.
Complete minimal surfaces in  .
Ann. of Math. (2), 92:335-374, 1970. MR 0270280 (42:5170) - 6.
- William H. Meeks III, Joaquín Pérez, and Antonio Ros.
Stable constant mean curvature surfaces,
preprint. - 7.
- Antonio Ros and Harold Rosenberg.
Properly embedded surfaces with constant mean curvature,
preprint. - 8.
- Harold Rosenberg.
Constant mean curvature surfaces in homogeneously regular  -manifolds.
Bull. Austral. Math. Soc., 74:227-238, 2006. MR 2260491 (2007g:53009) - 9.
- Richard Schoen.
Estimates for stable minimal surfaces in three-dimensional manifolds.
In Seminar on minimal submanifolds, volume 103 of Ann. of Math. Stud., pages 111-126. Princeton Univ. Press, 1983. MR 795231 (86j:53094)
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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
Email:
laurent.mazet@math.cnrs.fr
DOI:
10.1090/S0002-9939-09-09885-2
PII:
S 0002-9939(09)09885-2
Received by editor(s):
September 26, 2008,
Received by editor(s) in revised form:
January 7, 2009
Posted:
March 18, 2009
Communicated by:
Richard A. Wentworth
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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