Gradient Estimate and Liouville Property of L-pseudoharmonic Functions on a Complete Pseudohermitian Manifold with Bakry-Emery Pseudohermitian Ricci Curvature
Date Issued
2015
Date
2015
Author(s)
Yu, Li-Chung
Abstract
In this paper, we modify Yau''s method to discuss a gradient estimate of a nonnegative L-pseudoharmonic function on a oriented, complete, pseudohermitian manifold which satisfies Witten-sub-Laplacian comparison property. Since the manifold we considered in this paper is weighted manifold, the curvature we consider is not only Ricci curvature but Bakry-Emery Ricci curvature Ric_m,n (L). At the end of this paper, we can get that when the form 2Ric_m,n (L) - Tor(L) is bounded below, any gradient estimate of a nonnegative L-pseudoharmonic function is bounded. Moreover, we can then deduce Liouville property on such manifold with curvature satisfies 2Ric_m,n (L) > Tor(L).
Subjects
weighted manifold
CR manifold
Bakry-Emery Ricci curvature
L-harmonicfunction
gradient estimate
Type
thesis
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