## Asian Journal of Mathematics

### Subgradient Estimate and Liouville-type Theorem for the $CR$ Heat Equation on Heisenberg Groups

#### Abstract

In this paper, we first get a subgradient estimate of the $CR$ heat equation on a closed pseudohermitian $(2n + 1)$-manifold. Secondly, by deriving the $CR$ version of sub-Laplacian comparison theorem on an $(2n + 1)$-dimensional Heisenberg group $H^n$, we are able to establish a subgradient estimate and then the Liouville-type theorem for the $CR$ heat equation on $H^n$.

#### Article information

Source
Asian J. Math., Volume 14, Number 1 (2010), 41-72.

Dates
First available in Project Euclid: 8 October 2010

Chang, Shu-Cheng; Tie, Jingzhi; Wu, Chin-Tung. Subgradient Estimate and Liouville-type Theorem for the $CR$ Heat Equation on Heisenberg Groups. Asian J. Math. 14 (2010), no. 1, 41--72. https://projecteuclid.org/euclid.ajm/1286547518