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

TL;DR

This paper establishes gradient estimates, Harnack inequalities, and heat kernel bounds for positive solutions of the CR heat equation on complete noncompact pseudo-Hermitian manifolds, advancing understanding of geometric analysis in this setting.

Contribution

It introduces new Li-Yau type gradient estimates for the CR heat equation on noncompact pseudo-Hermitian manifolds, with applications to Harnack inequalities and heat kernel bounds.

Findings

Derived local and global gradient estimates

Established a Harnack inequality for positive solutions

Obtained upper bounds for the heat kernel

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.