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arXiv · 1207.4033

An Obata-type Theorem in CR Geometry

Song-Ying Li·Xiaodong Wang
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Abstract

We discuss a sharp lower bound for the first positive eigenvalue of the sublaplacian on a closed, strictly pseudoconvex pseudo-hermitian manifold of dimension $2m+1\geq 5$. We prove that the equality holds iff the manifold is equivalent to the CR sphere up to a scaling. The essential step is a characterization of the CR sphere when there is a nonzero function satisfying a certain overdetermined system.

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Song-Ying Li, Xiaodong Wang. 2013-08-14. An Obata-type Theorem in CR Geometry. https://arxiv.org/abs/1207.4033

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