An integral formula on the Heisenberg group

TL;DR

This paper proves a new integral identity on the Heisenberg group that generalizes a classical formula, with initial applications demonstrating its utility in sub-Riemannian geometry.

Contribution

It introduces a generalized integral formula on the Heisenberg group, extending Reilly's 1970s result, and explores its initial applications.

Findings

New integral identity on Hn

Generalizes Reilly's classical formula

Initial applications in sub-Riemannian geometry

Abstract

Let Hn denote the (2n + 1)-dimensional (sub-Riemannian) Heisenberg group. In this note, we shall prove an integral identity (see Theorem 1.2) which generalizes a formula obtained in the Seventies by Reilly. Some first applications will be given in Section 4.