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.
https://www.math.kth.se/GGlectures/poster21.pdf
Zoom: https://kth-se.zoom.us/j/61112478597
Lecture 1: Monday, May 24, 3.00–4.00 pm
Lecture 2: Tuesday, May 25, 2.00–3.00 pm
Lecture 3: Wednesday, May 26, 2.00–3.00 pm
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