Bismut-Stroock Hessian formulas and local Hessian estimates for heat semigroups and harmonic functions on Riemannian manifolds

2021/10/11 by Qin-Qian Chen, Chen, Qin-Qian, Lijuan Cheng +3 · 1 citation
Mathematics · #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2110.05131

Abstract

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 established by Stroock (1996) and removes in particular the compact manifold restriction. To demonstrate the potential of these formulas, we give as application explicit quantitative local estimates for the Hessian of the heat semigroup, as well as for harmonic functions on regular domains in Riemannian manifolds.

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