Georgia Institute of Technology College of Sciences

We prove a quantitative Brunn-Minkowski inequality for sets E and K,one of which, K, is assumed convex, but without assumption on the other set. We are primarily interested in the case in which K is a ball. We use this to prove an estimate on the remainder in the Riesz rearrangement inequality under certain conditions on the three functions involved that are relevant to a problem arising in statistical mechanics: This is joint work with Franceso Maggi.