Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Planar Wulff shape is unique equilibrium

Author(s): Frank Morgan
Journal: Proc. Amer. Math. Soc. 133 (2005), 809-813.
MSC (2000): Primary 49K99
Posted: September 20, 2004
Retrieve article in: PDF DVI PostScript

Abstract | References | Similar articles | Additional information

Abstract: In $\mathbf{R}^2$, for any norm, an immersed closed rectifiable curve in equilibrium for fixed area must be the Wulff shape (possibly with multiplicity).

References:

[A]
A. D. Aleksandrov, Uniqueness theorems for surfaces in the large. $V$, Vestnik Leningrad Univ. Mat. Mekh. Astronom. 13 (1958), 5-8; Amer. Math. Soc. Transl. (2) 21 (1962), 412-416. MR 27:698e

[BdC]
João Lucas Barbosa and Manfredo do Carmo, Stability of hypersurfaces with constant mean curvature, Math. Z. 185 (1984), 339-353. MR 85k:58021c

[K1]
Nicolaos Kapouleas, Compact constant mean curvature surfaces in Euclidean three-space, J. Diff. Geom. 33 (1991), 683-715. MR 93a:53007b

[K2]
Nicolaos Kapouleas, Constant mean curvature surfaces in Euclidean three-space, Bull. AMS 17 (1987), 318-326. MR 88g:53013

[M1]
Frank Morgan, Cylindrical surfaces of Delaunay, preprint (2003).

[M2]
Frank Morgan, Hexagonal surfaces of Kapouleas, Pacific J. Math., to appear.

[M3]
Frank Morgan, Riemannian Geometry: A Beginner's Guide, A K Peters, Ltd., 1998. MR 98i:53001

[P]
Bennett Palmer, Stability of the Wulff shape, Proc. AMS 126 (1998), 3661-3667. MR 99b:58055

[T]
Jean Taylor, Crystalline variational problems, Bull. AMS 84 (1978), 568-588. MR 58:12649

[W]
Henry C. Wente, Counterexample to a conjecture of H. Hopf, Pacific J. Math. 121 (1986), 193-243. MR 87d:53013

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 49K99

Retrieve articles in all Journals with MSC (2000): 49K99

Additional Information:

Frank Morgan
Affiliation: Department of Mathematics and Statistics, Williams College, Williamstown, Massachusetts 01267
Email: frank.morgan@williams.edu

DOI: 10.1090/S0002-9939-04-07661-0
PII: S 0002-9939(04)07661-0
Received by editor(s): March 30, 2003
Received by editor(s) in revised form: November 3, 2003
Posted: September 20, 2004
Communicated by: David Preiss
Copyright of article: Copyright 2004, Frank Morgan

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google