On the area of constant mean curvature discs and annuli with circular boundaries |
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| Authors: | Luis J Alías Bennett Palmer |
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| Institution: | (1) Departamento de Matemáticas, Universidad de Murcia, E-30100 Espinardo, Murcia, Spain (e-mail: ljalias@um.es) , ES;(2) Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, England (e-mail: Bennett.Palmer@durham.ac.uk) , GB |
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| Abstract: | It is still an open question whether a constant mean curvature (CMC) disc which is bounded by a circle is necessarily a spherical
cap or a flat disc. The authors together with López 1] recently showed that the only stable CMC discs which are bounded by
a circle are spherical caps. In this paper we derive lower bounds for the area of constant mean curvature discs and annuli
with circular boundaries in 3-dimensional space forms.
Received November 8, 1999; in final form January 18, 2000 / Published online March 12, 2001 |
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| Keywords: | Mathematics Subject Classification (2000): 53A10 53C42 |
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