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math.PR2021
Bismut-Stroock Hessian formulas and local Hessian estimates for heat semigroups and harmonic functions on Riemannian manifolds
Qin-Qian Chen, Li-Juan Cheng, Anton Thalmaier
In this article, we develop a martingale approach to localized Bismut-type Hessian formulas for heat semigroups on Riemannian manifolds. Our approach extends the Hessian formulas e…
math.DG2021★ 3 cited
Hessian heat kernel estimates and Calderón-Zygmund inequalities on complete Riemannian manifolds
Jun Cao, Li-Juan Cheng, Anton Thalmaier
We address some fundamental questions concerning geometric analysis on Riemannian manifolds. It has been asked whether the -Calderón-Zygmund inequalities extend to a reasonabl…
math.DG2021
Some inequalities on Riemannian manifolds linking Entropy,Fisher information, Stein discrepancy and Wasserstein distance
Li-Juan Cheng, Feng-Yu Wang, Anton Thalmaier
For a complete connected Riemannian manifold let be such that $μ(d x)={\rm e}^{-V(x)} \mbox{vol}(d x)$ is a probability measure on . Taking as reference me…