English

A CR invariant sphere theorem

Differential Geometry 2022-06-09 v2 Complex Variables Geometric Topology

Abstract

We prove that every closed, universally embeddable CR three-manifold with nonnegative Yamabe constant and positive total QQ^\prime-curvature is contact diffeomorphic to a quotient of the standard contact three-sphere. We also prove that every closed, embeddable CR three-manifold with zero Yamabe constant and nonnegative total QQ^\prime-curvature is CR equivalent to a compact quotient of the Heisenberg group with its flat CR structure.

Keywords

Cite

@article{arxiv.2204.02333,
  title  = {A CR invariant sphere theorem},
  author = {Jeffrey S. Case and Paul Yang},
  journal= {arXiv preprint arXiv:2204.02333},
  year   = {2022}
}

Comments

11 pages; added references related to the CR Positive Mass Theorem and the CR Yamabe constant of Rossi spheres

R2 v1 2026-06-24T10:38:47.687Z