WorkshopsYau's gradient estimate and Lioville theorem for positive psedoharmonic functions in a complete pseudohermitian manifold
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In this talk, I will discuss the Liouville property for sub- Laplacian in the standard Heisenberg manifolds. We first derive the sub-gradient estimate for positive pseudoharmonic functions in a complete pseudohermitian $(2n+1)$-manifold which satisfies the CR sub-Laplacian comparison property. Secondly, we obtain the CR sub-Laplacian comparison theorem in a class of complete noncompact pseudohermitian manifolds. Finally we have the natural analogue of Liouville-type theorems for the sub-Laplacian in a standard Heisenberg manifold. This is a joint work with Prof. Shu-Cheng Chang and Prof. Jingzhi Tie.
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Ting-Jung Kuo
2012-03-17
16:20:00 - 17:10:00
308 , Mathematics Research Center Building (ori. New Math. Bldg.)
In this talk, I will discuss the Liouville property for sub- Laplacian in the standard Heisenberg manifolds. We first derive the sub-gradient estimate for positive pseudoharmonic functions in a complete pseudohermitian $(2n+1)$-manifold which satisfies the CR sub-Laplacian comparison property. Secondly, we obtain the CR sub-Laplacian comparison theorem in a class of complete noncompact pseudohermitian manifolds. Finally we have the natural analogue of Liouville-type theorems for the sub-Laplacian in a standard Heisenberg manifold. This is a joint work with Prof. Shu-Cheng Chang and Prof. Jingzhi Tie.