Area formula for regular submanifolds of low codimension in Heisenberg groups

TL;DR

This paper derives an area formula for regular submanifolds in Heisenberg groups, using intrinsic differentiability and chain rules, applicable to arbitrary homogeneous distances.

Contribution

It introduces a new area formula for intrinsically regular submanifolds in Heisenberg groups, emphasizing differentiability and chain rule techniques.

Findings

Established an area formula for spherical measure in Heisenberg groups.

Proved differentiability properties of intrinsic graphs.

Applied chain rule for intrinsic differentiable functions.

Abstract

We establish an area formula for the spherical measure of intrinsically regular submanifolds of low codimension in Heisenberg groups. The spherical measure is computed with respect to an arbitrary homogeneous distance. Among the arguments of the proof, we point out the differentiability properties of intrinsic graphs and a chain rule for intrinsic differentiable functions.