Planar Wulff shape is unique equilibrium
HTML articles powered by AMS MathViewer
- by Frank Morgan PDF
- Proc. Amer. Math. Soc. 133 (2005), 809-813
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. D. Aleksandrov, Uniqueness theorems for surfaces in the large. I, Amer. Math. Soc. Transl. (2) 21 (1962), 341–354. MR 0150706, DOI 10.1090/trans2/021/09
- Hiroshi Mori, On surfaces of right helicoid type in $H^{3}$, Bol. Soc. Brasil. Mat. 13 (1982), no. 2, 57–62. MR 735120, DOI 10.1007/BF02584676
- Nicolaos Kapouleas, Complete constant mean curvature surfaces in Euclidean three-space, Ann. of Math. (2) 131 (1990), no. 2, 239–330. MR 1043269, DOI 10.2307/1971494
- Nicolaos Kapouleas, Constant mean curvature surfaces in Euclidean three-space, Bull. Amer. Math. Soc. (N.S.) 17 (1987), no. 2, 318–320. MR 903742, DOI 10.1090/S0273-0979-1987-15575-3
- Frank Morgan, Cylindrical surfaces of Delaunay, preprint (2003).
- Frank Morgan, Hexagonal surfaces of Kapouleas, Pacific J. Math., to appear.
- Frank Morgan, Riemannian geometry, 2nd ed., A K Peters, Ltd., Wellesley, MA, 1998. A beginner’s guide. MR 1600519
- Bennett Palmer, Stability of the Wulff shape, Proc. Amer. Math. Soc. 126 (1998), no. 12, 3661–3667. MR 1473676, DOI 10.1090/S0002-9939-98-04641-3
- Jean E. Taylor, Crystalline variational problems, Bull. Amer. Math. Soc. 84 (1978), no. 4, 568–588. MR 493671, DOI 10.1090/S0002-9904-1978-14499-1
- Henry C. Wente, Counterexample to a conjecture of H. Hopf, Pacific J. Math. 121 (1986), no. 1, 193–243. MR 815044
Additional Information
- Frank Morgan
- Affiliation: Department of Mathematics and Statistics, Williams College, Williamstown, Massachusetts 01267
- Email: frank.morgan@williams.edu
- Received by editor(s): March 30, 2003
- Received by editor(s) in revised form: November 3, 2003
- Published electronically: September 20, 2004
- Communicated by: David Preiss
- © Copyright 2004 Frank Morgan
- Journal: Proc. Amer. Math. Soc. 133 (2005), 809-813
- MSC (2000): Primary 49K99
- DOI: https://doi.org/10.1090/S0002-9939-04-07661-0
- MathSciNet review: 2113931