The Brunn-Minkowski inequality for the first eigenvalue of the Ornstein-Uhlenbeck operator and log-concavity of the relevant eigenfunction

Andrea Colesanti, Elisa Francini, Galyna Livshyts +1

We prove that the first (nontrivial) Dirichlet eigenvalue of the Ornstein-Uhlenbeck operator $$L(u)=\Delta u-⟨\nabla u,x⟩,$$ as a function of the domain, is convex with r…