Uniformization of spherical CR manifolds

Jih Hsin Cheng, Hung Lin Chiu, Paul Yang

Research output: Contribution to journalArticle

16 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)182-216
Number of pages35
JournalAdvances in Mathematics
Volume255
DOIs
StatePublished - 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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