Anton Thalmaier (University of Luxembourg)
Abstract: We explain some new formulas for the Hessian of the heat semigroup generated by the Laplace-Beltrami operator on a Riemannian manifold and describe geometric applications related to Calderón-Zygmund type inequalities. Our approach relies on probabilistic methods from Stochastic Analysis.
If time permits we also describe new versions of log-Sobolev and transportation inequalities connecting relative entropy, Stein discrepancy and relative Fisher information on Riemannian manifolds.