An Optimal Gap Theorem in a Complete Strictly Pseudoconvex CR Manifold

Shu-Cheng Chang; Yen-Wen Fan

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arXiv · 1504.00786

An Optimal Gap Theorem in a Complete Strictly Pseudoconvex CR Manifold

Shu-Cheng Chang·Yen-Wen Fan

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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.

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BibTeX RIS

Shu-Cheng Chang, Yen-Wen Fan. 2015-04-03. An Optimal Gap Theorem in a Complete Strictly Pseudoconvex CR Manifold. https://arxiv.org/abs/1504.00786

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