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

DOI:
https://doi.org/10.1090/S0002-9939-99-04950-3

MathSciNet review:
1618705

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Abstract: In this paper we study stable constant mean curvature surfaces in the Euclidean space 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 and the hyperbolic space .

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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:
https://doi.org/10.1090/S0002-9939-99-04950-3

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