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Stable constant mean curvature surfaces with circular boundary

Author(s): Luis J. Alías; Rafael López; Bennett Palmer
Journal: Proc. Amer. Math. Soc. 127 (1999), 1195-1200.
MSC (1991): Primary 53A10; Secondary 53C42
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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: 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
Copyright of article: Copyright 1999, American Mathematical Society

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