### 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 S^{2n+1} is the standard unit sphere in complex n+1-space C^{n+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.

Original language | English (US) |
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Pages (from-to) | 182-216 |

Number of pages | 35 |

Journal | Advances in Mathematics |

Volume | 255 |

DOIs | |

State | Published - Apr 1 2014 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Keywords

- CR developing map
- CR sublaplacian
- Green's function
- Paneitz-like operator
- Spherical CR manifold

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## Cite this

Cheng, J. H., Chiu, H. L., & Yang, P. (2014). Uniformization of spherical CR manifolds.

*Advances in Mathematics*,*255*, 182-216. https://doi.org/10.1016/j.aim.2014.01.002