The Neumann problem on the Clifford torus in $\mathbb{S}^3$

Jeffrey S. Case; Eric Chen; Yi Wang; Paul Yang; Po-Lam Yung

The Neumann problem on the Clifford torus in $\mathbb{S}^3$

Analysis of PDEs 2023-04-07 v1 Complex Variables Differential Geometry

Authors: Jeffrey S. Case , Eric Chen , Yi Wang , Paul Yang , Po-Lam Yung

Abstract

We discuss the solution of the Neumann problem associated with the CR Yamabe operator on a subset $\Omega$ of the CR manifold $\mathbb{S}^3$ bounded by the Clifford torus $\Sigma$ . We also discuss the Yamabe-type problem of finding a contact form on $\Omega$ which has zero Tanaka--Webster scalar curvature and for which $\Sigma$ has constant $p$ -mean curvature.

Keywords

yamabe problem

Cite

@article{arxiv.2304.02823,
  title  = {The Neumann problem on the Clifford torus in $\mathbb{S}^3$},
  author = {Jeffrey S. Case and Eric Chen and Yi Wang and Paul Yang and Po-Lam Yung},
  journal= {arXiv preprint arXiv:2304.02823},
  year   = {2023}
}

Comments

36 pages

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