Dmitry Faifman

The Faber-Krahn position of convex bodies and Gaussian measure inequalities

We say that a convex body is in Faber-Krahn position if it minimizes the first Dirichlet eigenvalue within its volume-preserving linear orbit. We prove that this position is unique up to orthogonal transformations, answering a question of Schmuckenschlaeger from 2011. This is a corollary of a new log-convexity property...