Geometric stability of the Coulomb energy

  • Almut Burchard
  • Gregory R. Chambers


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 Classification

26D15 (31B05, 35J35, 51M16) 



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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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada
  2. 2.Department of MathematicsUniversity of ChicagoChicagoUSA

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