A CR invariant sphere theorem

Jeffrey S. Case; Paul Yang

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arXiv · 2204.02333

A CR invariant sphere theorem

Jeffrey S. Case·Paul Yang

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Abstract

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

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Jeffrey S. Case, Paul Yang. 2022-04-05. A CR invariant sphere theorem. https://arxiv.org/abs/2204.02333

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