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Stability of the Wulff Shape
Author(s):
Bennett
Palmer
Journal:
Proc. Amer. Math. Soc.
126
(1998),
3661-3667.
MSC (1991):
Primary 53A10;
Secondary 52A15
MathSciNet review:
1473676
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Abstract:
We consider the functional of a hypersurface, given by a convex elliptic integrand with a volume constraint. We show that, up to homothety and translation, the only closed, oriented, stable critical point is the Wulff shape.
References:
- 1.
- Federer, H. Geometric Measure Theory, Springer-Verlag, New York 1969. MR 41:1976
- 2.
- Barbosa, J.L. and doCarmo, M. Stability of hypersurfaces of constant mean curvature , Math. Zeit., 185 (1984) 339-353. MR 85k:58021
- 3.
- Taylor, J.Crystalline variational problems, Bull. Amer. Math. Soc. 84(1978),568-588. MR 58:12649
- 4.
- Brothers, J.,E. and Morgan, F.The isoperimetric theorem for general integrands, Michigan Math. J. 41(1994)419-431. MR 95g:49080
- 5.
- Wente, H. A note on the stability theorem of J. L. Barbosa and M. Do Carmo for closed surfaces of constant mean curvature. Pac. Math. J. ,Vol.147,No.2,1991. MR 92g:53010
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Additional Information:
Bennett
Palmer
Affiliation:
Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, England
Email:
bennett.palmer@durham.ac.uk
DOI:
10.1090/S0002-9939-98-04641-3
PII:
S 0002-9939(98)04641-3
Received by editor(s):
April 29, 1997
Additional Notes:
The author was supported by a DGICYT Grant No. SAB95-0494
Communicated by:
Peter Li
Copyright of article:
Copyright
1998,
American Mathematical Society
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