- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- BIRS Workshop Lecture Videos /
- Yau’s Gradient Estimate and Liouville Theorem for Positive...
Open Collections
BIRS Workshop Lecture Videos
BIRS Workshop Lecture Videos
Yau’s Gradient Estimate and Liouville Theorem for Positive Pseudoharmonic Functions in a Complete Pseudohermitian manifold Tie, Jingzhi
Description
I will introduce the basic notion of pseudhermitian manifold first and derive the sub-gradient estimate for positive pseudoharmonic functions in a complete pseudohermitian (2n + 1)-manifold (M, J, θ) which satisfies the CR sub-Laplacian comparison property. It is served as the CR analogue of Yau’s gradient estimate. Secondly, we obtain the Bishop-type sub-Laplacian comparison theorem in a class of complete noncompact pseudohermitian manifolds. Finally we will show the natural analogue of Liouville-type theo- rems for the sub-Laplacian in a complete pseudohermitian manifold of vanishing pseudohermitian torsion tensors and nonnegative pseudohermitian Ricci curvature tensors. This a joint project with Shu-Cheng Chang and Ting-Jung Kuo of National Taiwan University.
Item Metadata
Title |
Yau’s Gradient Estimate and Liouville Theorem for Positive Pseudoharmonic Functions in a Complete Pseudohermitian manifold
|
Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
|
Date Issued |
2015-10-19T16:33
|
Description |
I will introduce the basic notion of pseudhermitian manifold first and derive the sub-gradient estimate for positive pseudoharmonic functions in a complete pseudohermitian (2n + 1)-manifold (M, J, θ) which satisfies the CR sub-Laplacian comparison property. It is served as the CR analogue of Yau’s gradient estimate. Secondly, we obtain the Bishop-type sub-Laplacian comparison theorem in a class of complete noncompact pseudohermitian manifolds. Finally we will show the natural analogue of Liouville-type theo- rems for the sub-Laplacian in a complete pseudohermitian manifold of vanishing pseudohermitian torsion tensors and nonnegative pseudohermitian Ricci curvature tensors. This a joint project with Shu-Cheng Chang and Ting-Jung Kuo of National Taiwan University.
|
Extent |
39 minutes
|
Subject | |
Type | |
File Format |
video/mp4
|
Language |
eng
|
Notes |
Author affiliation: University of Georgia
|
Series | |
Date Available |
2016-04-19
|
Provider |
Vancouver : University of British Columbia Library
|
Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
DOI |
10.14288/1.0228641
|
URI | |
Affiliation | |
Peer Review Status |
Unreviewed
|
Scholarly Level |
Faculty
|
Rights URI | |
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International