Isoperimetric Problem with a Coulomb Repulsive Term

摘要

We consider a non-local isoperimetric problem with a repulsive Coulomb term. In dimension three, this corresponds to Gamow's famous liquid drop model. We show that, whenever the mass is small, the ball is the unique minimizer of the problem, and thus give a partial answer to a conjecture by Choksi and Peletier. The proof is based on a strong version of a quantitative isoperimetric inequality introduced in [6].