Green's function for certain domains in the Heisenberg Group $\mathbb H_n$

TL;DR

This paper derives explicit smooth Green's functions for specific domains in the Heisenberg group using Kelvin R-transform, enhancing analytical tools for sub-Riemannian geometry.

Contribution

It introduces a method to explicitly compute Green's functions for annular and strip domains in the Heisenberg group, utilizing Kelvin R-transform techniques.

Findings

Explicit Green's functions for annular domains

Explicit Green's functions for infinite strip domains

Application of Kelvin R-transform in sub-Riemannian geometry

Abstract

We obtain explicit smooth Green's functions for annular domain and infinite strip by using kelvin $R$-transform in the Heisenberg group $\H_n$.