An Upper Bound for Hessian Matrices of Positive Solutions of Heat Equations

2012/12/12 by Han, Qing, Zhang, Qi S · 3 citations
#35K05 #53C44 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1212.2723

Abstract

We prove global and local upper bounds for the Hessian of log positive solutions of the heat equation on a Riemannian manifold. The metric is either fixed or evolves under the Ricci flow. These upper bounds supplement the well-known global lower bound.

Cited by

• Backward Harnack inequality and Hamilton estimates for heat type equations
• Optimal Hamilton-type gradient estimates and large time heat kernel bounds for noncompact manifolds
• Hessian matrix estimates of heat-type equations via Bismut-Stroock Hessian formula

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• Hessian estimates for the conjugate heat equation coupled with the Ricci flow
• Hessian matrix estimates of heat-type equations via Bismut-Stroock Hessian formula
• Li-Yau-Hamilton estimates and Bakry-Emery Ricci curvature
• A matrix Harnack inequality for semilinear heat equations
• Optimal Hamilton-type gradient estimates and large time heat kernel bounds for noncompact manifolds