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 -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 -curvature is CR equivalent to a compact quotient of the Heisenberg group with its flat CR structure.
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