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A round ball uniquely minimizes gravitational potential energy

Author(s): Frank Morgan
Journal: Proc. Amer. Math. Soc. 133 (2005), 2733-2735.
MSC (2000): Primary 76U05, 49Q10, 85A30, 53C80
Posted: April 12, 2005
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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 and density at most 1, a round ball of unit density uniquely minimizes gravitational potential energy.

References:

[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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