Submanifolds with boundary in sub-Riemannian Heisenberg Groups

TL;DR

This paper explores submanifolds with boundary in sub-Riemannian Heisenberg groups, establishing their properties and presenting a Stokes' Theorem involving Rumin's differential forms, advancing geometric analysis in this setting.

Contribution

It introduces the concept of submanifolds with boundary in Heisenberg groups and proves a Stokes' Theorem for these structures using Rumin's differential forms.

Findings

Defined intrinsic $C^1$ submanifolds with boundary in Heisenberg groups

Provided examples of such submanifolds

Proved a Stokes' Theorem involving Rumin's differential forms

Abstract

We discuss the notion of submanifolds with boundary with intrinsic $C^1$ regularity in sub-Riemannian Heisenberg groups and we provide some examples. Eventually, we present a Stokes' Theorem for such submanifolds involving the integration of Rumin's differential forms in Heisenberg groups.