A round ball uniquely minimizes gravitational potential energy
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- by Frank Morgan PDF
- Proc. Amer. Math. Soc. 133 (2005), 2733-2735
Abstract:
We give a proof following Carleman that among measurable bodies in $\mathbf {R}^3$ of mass $m_0$ and density at most 1, a round ball of unit density uniquely minimizes gravitational potential energy.References
- Wilhelm Blaschke, Eine isoperimetrische Eigenschaft des Kreises, Math. Z. 1 (1918), 52–57.
- T. Carleman, Über eine isoperimetrische Aufgabe und ihre physikalischen Anwendungen, Math. Z. 3 (1919), 1–7.
- S. Chandrasekhar, Ellipsoidal figures of equilibrium—an historical account, Comm. Pure Appl. Math. 20 (1967), 251–265. MR 213075, DOI 10.1002/cpa.3160200203
- Frank Morgan, The perfect shape for a rotating rigid body, Math. Magazine 75 (February, 2002), 30–32.
- H. Poincaré, Figures d’Equilibre d’une Masse, Paris, Gauthier-Villars, 1902.
Additional Information
- Frank Morgan
- Affiliation: Department of Mathematics and Statistics, Williams College, Williamstown, Massachusetts 01267
- Email: Frank.Morgan@williams.edu
- Received by editor(s): January 14, 2002
- Published electronically: April 12, 2005
- Communicated by: Wolfgang Ziller
- © Copyright 2005 by Frank Morgan
- Journal: Proc. Amer. Math. Soc. 133 (2005), 2733-2735
- MSC (2000): Primary 76U05, 49Q10, 85A30, 53C80
- DOI: https://doi.org/10.1090/S0002-9939-05-08070-6
- MathSciNet review: 2146221