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Geometric stability of the Coulomb energy

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Abstract

The Coulomb energy of a charge that is uniformly distributed on some set is maximized (among sets of given volume) by balls. It is shown here that near-maximizers are close to balls.

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Acknowledgments

The authors thank Nicola Fusco, Francesco Maggi, and Aldo Pratelli for sharing their manuscript [10], and for their hospitality on several occasions. This work was supported in part by the Federal Government of Canada through an NSERC CGS Fellowship (G.R.C.) and a Discovery Grant (A.B.), and by the Province of Ontario through an OGS Fellowship (G.R.C.).

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, 40 St. George Street, Rm. 6290, Toronto, Ontario, M5S 2E4, Canada

    Almut Burchard & Gregory R. Chambers

  2. Department of Mathematics, University of Chicago, 5734 S. University Avenue, Room 208C, Chicago, IL, 60637, USA

    Gregory R. Chambers

Authors
  1. Almut Burchard
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  2. Gregory R. Chambers
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Correspondence to Almut Burchard.

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Communicated by L. Ambrosio.

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Burchard, A., Chambers, G.R. Geometric stability of the Coulomb energy. Calc. Var. 54, 3241–3250 (2015). https://doi.org/10.1007/s00526-015-0900-8

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  • DOI: https://doi.org/10.1007/s00526-015-0900-8

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