A Neumann problem on the domain in a 3-sphere bounded by the Clifford torus

The Clifford torus is the simplest and the most symmetric torus embedded in \(\mathbb R^4\). It is the product of two circles of the same radius, and arises as the boundary of a domain in the \(3\)-sphere. In this talk I will discuss how single layer potentials can be used to solve a subelliptic Neumann boundary value problem for this domain. The motivation comes from CR geometry, but I will focus on the underlying analysis and raise some interesting questions.

This is joint work with Jeffrey Case, Eric Chen, Yi Wang and Paul Yang.