A quantitative Brunn-Minkowski inequality and estimates on the the remainder in the Riesz rearrangement inequality

Non-equilibrium Dynamics and Random Matrices
Topic:A quantitative Brunn-Minkowski inequality and estimates on the the remainder in the Riesz rearrangement inequality
Speaker:Eric Carlen
Affiliation:Rutgers University
Date:Tuesday, January 21
Time/Room:2:00pm - 3:00pm/S-101

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.