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Hessian matrix estimates of heat-type equations via Bismut-Stroock Hessian formula (2506.11805v1)
Published 13 Jun 2025 in math.AP and math.DG
Abstract: In this paper, we establish a new global Hessian matrix estimate for heat-type equations on Riemannian manifolds using a Bismut-type Hessian formula. Our results feature fully explicit coefficients as well as delay / growth rate functions. These estimates yield two key applications: a novel backward weak Harnack inequality and a precise pointwise Hessian estimate for eigenfunctions.