Gradient Estimates For The CR Heat Equation On Complete noncompact Pseudo-Hermitian Manifolds

2023/02/20 by Dong, Yuxin, Ren, Yibin, Zhao, Biqiang
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2302.09733

Abstract

In this paper, we derive local and global Li-Yau type gradient estimates for the positive solutions of the CR heat equation on complete noncompact pseudo-Hermitian manifolds. As applications of the gradient estimates, we give a Harnack inequality for the positive solutions of the CR heat equation, and then obtain an upper bound estimate for the corresponding heat kernel.

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