The Functional Volume Product Under Heat Flow

Explore the monotonicity of the functional volume product along the Fokker-Planck heat flow in this 29-minute lecture by Hirsoshi Tsuji from the Hausdorff Center for Mathematics. Delve into a joint work with Shohei Nakamura, examining the regularized functional volume product inspired by Bobkov-Gentil-Ledoux's research. Discover how this approach not only demonstrates the monotonicity of the functional volume product but also yields an improved Borell's hypercontractivity and establishes a lower bound for the quasi-norm of the Laplace transform.