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<p>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 time reversed Harnack-type inequality and a precise pointwise Hessian estimate for eigenfunctions.</p>

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Hessian Matrix Estimates of Heat-Type Equations Via Bismut–Stroock Hessian Formula

  • 期刊论文

  • 发表日期：

    2026年6月26日

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  • Li-Juan Cheng,
  • Rui-Yu Yang

摘要

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 time reversed Harnack-type inequality and a precise pointwise Hessian estimate for eigenfunctions.