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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Stable constant mean curvature surfaces
with circular boundary


Authors: Luis J. Alías, Rafael López and Bennett Palmer
Journal: Proc. Amer. Math. Soc. 127 (1999), 1195-1200
MSC (1991): Primary 53A10; Secondary 53C42
MathSciNet review: 1618705
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Abstract: In this paper we study stable constant mean curvature surfaces in the Euclidean space $\mathbf{R}^3$ with circular boundary. We show that in the case of genus zero, the only such surfaces are the spherical caps and the flat discs. We also extend this result to the case of surfaces in the other space forms, namely the sphere $\mathbf{S}^3$ and the hyperbolic space $\mathbf{H}^3$.


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Additional Information

Luis J. Alías
Affiliation: Departamento de Matemáticas, Universidad de Murcia, 30100 Espinardo, Murcia, Spain
Email: ljalias@fcu.um.es

Rafael López
Affiliation: Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain
Email: rcamino@ugr.es

Bennett Palmer
Affiliation: Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, England
Email: bennett.palmer@durham.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04950-3
PII: S 0002-9939(99)04950-3
Received by editor(s): July 24, 1997
Additional Notes: The first author was partially supported by DGICYT Grant No. PB94-0750-C02-02 and Consejería de Educación y Cultura CARM Grant No. PB/5/FS/97, Programa Séneca (PRIDTYC)
The second author was partially supported by DGICYT Grant No PB94-0796.
The third author was supported by a DGICYT Grant No. SAB95-0494.
Communicated by: Peter Li
Article copyright: © Copyright 1999 American Mathematical Society