# Analysis Seminar

#### A Quantitative Brunn-Minkowski Inequality and Estimates on the the Remainder in the Riesz Rearrangement Inequality

Speaker: Eric Carlen, Rutgers University

Location: Warren Weaver Hall 1302

Date: Thursday, February 6, 2014, 11 a.m.

Synopsis:

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 Reisz 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.