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Stable surfaces with constant anisotropic mean curvature and circular boundary


Authors: Miyuki Koiso and Bennett Palmer
Journal: Proc. Amer. Math. Soc. 141 (2013), 3817-3823
MSC (2010): Primary 49Q10
DOI: https://doi.org/10.1090/S0002-9939-2013-11892-7
Published electronically: July 25, 2013
MathSciNet review: 3091771
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that for an axially symmetric anisotropic surface energy, only stable disc-type surfaces with constant anisotropic mean curvature bounded by a circle which lies in a plane orthogonal to the rotation axis of the Wulff shape are rescalings of parts of the Wulff shape and the flat disc.


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Additional Information

Miyuki Koiso
Affiliation: Institute of Mathematics for Industry, Kyushu University & PRESTO, JST, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
Email: koiso@math.kyushu-u.ac.jp

Bennett Palmer
Affiliation: Department of Mathematics, Idaho State University, Pocatello, Idaho 83209
Email: palmbenn@isu.edu

DOI: https://doi.org/10.1090/S0002-9939-2013-11892-7
Received by editor(s): January 9, 2012
Published electronically: July 25, 2013
Additional Notes: The first author was partially supported by Grant-in-Aid for Challenging Exploratory Research No. 22654009 of the Japan Society for the Promotion of Science
Communicated by: Michael Wolf
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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