Open Collections

Yau’s Gradient Estimate and Liouville Theorem for Positive Pseudoharmonic Functions in a Complete Pseudohermitian manifold

Banff International Research Station for Mathematical Innovation and Discovery

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.

Mathematics; Several complex variables and analytic spaces; Partial differential equations; Classical analysis

video/mp4

Author affiliation: University of Georgia

2016-04-19

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/57674

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/