An Optimal Gap Theorem in a Complete Strictly Pseudoconvex CR (2n+1)-Manifold

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 pseudoconvex CR ( 2 n + 1 ) -manifold with nonneg...

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Bibliographic Details
Published in:The Journal of geometric analysis 2016-07, Vol.26 (3), p.2425-2449
Main Authors: Chang, Shu-Cheng, Fan, Yen-Wen
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Global Analysis and Analysis on Manifolds
Mathematics
Mathematics and Statistics
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Summary: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 pseudoconvex CR ( 2 n + 1 ) -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 r centered at some point o decays as o r - 2 , then the manifold is flat.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-015-9632-4