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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

A round ball uniquely minimizes gravitational potential energy


Author: Frank Morgan
Journal: Proc. Amer. Math. Soc. 133 (2005), 2733-2735
MSC (2000): Primary 76U05, 49Q10, 85A30, 53C80
Published electronically: April 12, 2005
MathSciNet review: 2146221
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [B] Wilhelm Blaschke, Eine isoperimetrische Eigenschaft des Kreises, Math. Z. 1 (1918), 52-57.
  • [C] T. Carleman, Über eine isoperimetrische Aufgabe und ihre physikalischen Anwendungen, Math. Z. 3 (1919), 1-7.
  • [Ch] S. Chandrasekhar, Ellipsoidal figures of equilibrium—an historical account, Comm. Pure Appl. Math. 20 (1967), 251–265. MR 0213075 (35 #3940)
  • [M] Frank Morgan, The perfect shape for a rotating rigid body, Math. Magazine 75 (February, 2002), 30-32.
  • [P] H. Poincaré, Figures d'Equilibre d'une Masse, Paris, Gauthier-Villars, 1902.

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Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08070-6
PII: S 0002-9939(05)08070-6
Keywords: Rotating fluids, rigid body, gravitational potential energy
Received by editor(s): January 14, 2002
Published electronically: April 12, 2005
Communicated by: Wolfgang Ziller
Article copyright: © Copyright 2005 by Frank Morgan