Subgradient Estimate and Liouville-type Theorem for the $CR$ Heat Equation on Heisenberg Groups
Chang, Shu-Cheng ; Tie, Jingzhi ; Wu, Chin-Tung
Asian J. Math., Tome 14 (2010) no. 1, p. 41-72 / Harvested from Project Euclid
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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 $H^n$.
Publié le : 2010-03-15
Classification:  Subgradient estimate,  Liouville-type theorem,  heat kernel,  pseudohermitian manifold,  Heisenberg group,  $CR$-pluriharmonic,  $CR$-Paneitz operator,  sub-Laplacian,  Li-Yau Harnack inequality,  32V05,  32V20,  53C56 
@article{1286547518,
     author = {Chang, Shu-Cheng and Tie, Jingzhi and Wu, Chin-Tung},
     title = {Subgradient Estimate and Liouville-type Theorem for the $CR$ Heat Equation on Heisenberg Groups},
     journal = {Asian J. Math.},
     volume = {14},
     number = {1},
     year = {2010},
     pages = { 41-72},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1286547518}
}

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., Tome 14 (2010) no. 1, pp.  41-72. http://gdmltest.u-ga.fr/item/1286547518/