Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 223-256 |
| Number of pages | 34 |
| Journal | Asian Journal of Mathematics |
| Volume | 22 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2018 |
Keywords
- Bakry-Emery Pseudohermitian Ricci Curvature
- CR heat equation
- Harnack inequality
- Li-Yau gradient estimate
- Perelman Entropy formulae
- Pseudohermitian manifold
- Witten Laplacian
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics