The Neumann problem on the domain in 𝕊3 bounded by the Clifford torus

Abstract

Abstract In this study, the solution of the Neumann problem associated with the CR Yamabe operator on a subset Ω \Omega of the CR manifold S 3 {{\mathbb{S}}}^{3} bounded by the Clifford torus Σ \Sigma is discussed. The Yamabe-type problem of finding a contact form on Ω \Omega which has zero Tanaka-Webster scalar curvature and for which Σ \Sigma has a constant p p -mean curvature is also discussed.