In this paper, we derive the sub-gradient estimate of the CR heat equation associated with the Witten sub-Laplacian via the Bakry-Emery Pseudohermitian Ricci Curvature. With its applications, we first get a Harnack inequality for the positive solution of this CR heat equation in a closed pseudohermitian (2n + 1)-manifold. Secondly, we obtain Perelman-type linear entropy formulae for this CR heat equation.
ASJC Scopus subject areas
- Applied Mathematics