An Optimal Gap Theorem in a Complete Strictly Pseudoconvex CR Manifold

2015/04/03 by Shu-Cheng Chang, Chang, Shu-Cheng, Yen-Wen Fan +1
Mathematics · #32V05 (Primary) #32V20 #53C56 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #Point processes and geometric inequalities #math.DG #msc:32V05 #msc:32V20 #msc:53C56

paper · pdf · doi:10.48550/arxiv.1504.00786

21 pages

arxiv created 2015/04/03 · openalex publication_date 2015/04/03 · arxiv updated 2015/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, by applying a linear trace Li-Yau-Hamilton inequality for a positive (1,1)-form solution of the CR Hodge-Laplace heat equation and monotonicity of the heat equation deformation, we obtain an optimal gap theorem for a complete strictly pseudocovex CR manifold with nonnegative pseudohermitian bisectional curvature and vanishing torsion. We prove that if the average of the Tanaka-Webster scalar curvature over a ball of radius centered at some point o decays as o(r^-2), then the manifold is flat.

Citations

• On the parabolic kernel of the Schrödinger operator

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