Discoveries / analysis

Uniqueness of the Faber–Krahn Position of Convex Bodies

A convex body is in Faber-Krahn position if it minimizes the first Dirichlet eigenvalue within its volume-preserving linear orbit. The paper proves this position is unique up to orthogonal transformations, answering a question of Schmuckenschläger from 2011, via a new log-convexity property of the first eigenvalue under positive definite linear deformations.