Almut Burchard (Toronto)

Title: A geometric stability result for Riesz-potentials
Abstract: Riesz' rearrangement inequality implies that integral functionals (such as the Coulomb energy of a charge distribution) that are defined by a pair interaction potential (such as the Newton potential) which decreases with distance are maximized (under appropriate constraints) only by densities that are radially decreasing about some point. I will describe recent and ongoing work with Greg Chambers on the stability of this inequality for the special case of the Riesz-potentials in n dimensions (given by the kernels |x-y|^-(n-s)), for densities that are uniform on a set of given volume. For 1< s < n, we bound the square of the symmetric difference of a set from a ball by the difference in energy of the corresponding uniform distribution from that of the ball.