Asian Journal of Mathematics

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

Chin-Tung Wu, Shu-Cheng Chang, and Jingzhi Tie

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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

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1286547518

Mathematical Reviews number (MathSciNet)
MR2726594

Zentralblatt MATH identifier
1214.32011

Subjects
Primary: 32V05: CR structures, CR operators, and generalizations 32V20: Analysis on CR manifolds
Secondary: 53C56: Other complex differential geometry [See also 32Cxx]

Keywords
Subgradient estimate Liouville-type theorem heat kernel pseudohermitian manifold Heisenberg group $CR$-pluriharmonic $CR$-Paneitz operator sub-Laplacian Li-Yau Harnack inequality

Citation

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


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