Geometric stability of the Coulomb energy
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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.
Mathematics Subject Classification26D15 (31B05, 35J35, 51M16)
The authors thank Nicola Fusco, Francesco Maggi, and Aldo Pratelli for sharing their manuscript , 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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