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Uniformization of spherical CR manifolds

Author(s): Cheng, Jih-Hsin; Chiu, Hung-Lin; Yang, Paul C.

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Abstract: Let M be a closed (compact with no boundary) spherical CR manifold of dimension 2n+1. Let (M) over tilde be the universal covering of M. Let Phi denote a CR developing map Phi : (M) over tilde -> S2n+1 where S2n+1 is the standard unit sphere in complex n+1-space Cn+1. Suppose that the CR Yamabe invariant of M is positive. Then we show that Phi is injective for n greater than or similar to 3. In the case n = 2, we also show that 41. is injective under the condition: s(M) < 1 where s(M) means the minimum exponent of the integrability of the Green’s function for the CR invariant sublaplacian on <(M)over tilde>. It then follows that M is uniformizable. (C) 2014 Elsevier Inc. All rights reserved.
Publication Date: 1-Apr-2014
Electronic Publication Date: 23-Jan-2014
Citation: Cheng, Jih-Hsin, Chiu, Hung-Lin, Yang, Paul. (2014). Uniformization of spherical CR manifolds. ADVANCES IN MATHEMATICS, 255 (182 - 216). doi:10.1016/j.aim.2014.01.002
DOI: doi:10.1016/j.aim.2014.01.002
ISSN: 0001-8708
EISSN: 1090-2082
Pages: 182 - 216
Language: English
Type of Material: Journal Article
Journal/Proceeding Title: ADVANCES IN MATHEMATICS
Version: Author's manuscript

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