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Isoperimetric problem with a Coulombic repulsive term (1207.0715v1)

Published 3 Jul 2012 in math.AP

Abstract: We consider a non-local isoperimetric problem with a repulsive Coulombic term. In dimension three this corresponds to the Gamow's famous liquid drop model. We show that whenever the mass is small the ball is the unique minimizer of the problem. The proof is based on a strong version of a quantitative isoperimetric inequality.