Description
The Brunn-Minkowski inequality proved by Minkowski around 1900 for convex bodies of the n-dimensional Euclidean space is a generalization of the Isoperimetric inequality. Minkowski himself used the Brunn-Minkowski to solve some special cases of the "Minkowski problem", a Monge-Ampere type partial differential equation on the (n-1)-dimensional sphere. The full solution of the Minkowski problem was developed among others by Alexandrov, and Abel Prize laureates Nirenberg and Caffarelli by 1990. The main focus of the talk is on the Logarithmic-Brunn-Minkowski conjecture due to Boroczky, Lutwak, Yang, Zhang from 2013, where a strengthened version of the Brunn-Minkowski inequality for origin symmetric convex bodies is equivalent to the uniqueness of the solution of certain Monge-Ampere equation (the "logarithmic Minkowski problem") on the sphere.
https://us06web.zoom.us/j/87644664502?pwd=n72XjvvipnpGOhzxaomXq6Cb0bduCO.1
Meeting ID: 876 4466 4502
Passcode: 022053