Uniqueness of a smooth convex body with uniform cone volume measure in the neighborhood of a ball
Connections for Women: geometry and probability in high dimensions August 17, 2017 - August 18, 2017
cone volume measure
We prove that in every n-dimensional there exists a constant c=c(n)>0 so that in the c(n)-neighborhood of a ball, the only convex body with uniform cone volume measure is the ball. The goal of the talk will be to give an insight into some analytic aspects of the Log-Brunn-Minkowski and Log-Minkowski conjectures made by Boroczky, Lutwak, Yang and Zhang. This talk is based on the joint papers with Colesanti, Marsiglietti and Colesanti.
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