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

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.

36 pages