Uniformization of spherical CR manifolds

Jih-Hsin Cheng,Hung-Lin Chiu,Paul Yang

doi:10.1016/j.aim.2014.01.002

Jih-Hsin Cheng, Hung-Lin Chiu + Show 1 more

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https://doi.org/10.1016/j.aim.2014.01.002

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Journal: Advances in Mathematics	Publication Date: Jan 23, 2014
Citations: 32	License type: elsevier-specific: oa user license

Affiliation: National Central University, Princeton University

Abstract

Let M be a closed (compact with no boundary) spherical CR manifold of dimension 2n+1. Let M˜ be the universal covering of M. Let Φ denote a CR developing mapΦ:M˜→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 Φ is injective for n⩾3. In the case n=2, we also show that Φ 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˜. It then follows that M is uniformizable.

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