Lectures in Mathematics
May 24–26, 2021
QUANTITATIVE STABILITY IN GEOMETRIC AND FUNCTIONAL INEQUALITIES
Geometric and functional inequalities play a crucial role in several problems arising in analysis and geometry. The issue of the sharpness of a constant, as well as the characterization of minimizers, is a classical and important question. More recently, there has been a growing interest in studying the stability of such inequalities. The basic question one wants to address is the following:
Suppose we are given a functional inequality for which minimizers are known. Can we quantitatively show that if a function “almost attains the equality,” then it is close to one of the minimizers?
In this series of lectures, I will first give an overview of this beautiful topic and then discuss some recent results concerning the Sobolev, isoperimetric, and Brunn–Minkowski inequalities.
Monday, May 24, 3.00–4.00 pm
Tuesday, May 25, 2.00–3.00 pm
Wednesday, May 26, 2.00–3.00 pm