The Area Formula for Lipschitz Mappings of Carnot--Carath\'{e}odory Spaces

TL;DR

This paper establishes a sub-Riemannian area formula for Lipschitz mappings in equiregular Carnot--Carathéodory spaces, extending classical geometric measure theory into the sub-Riemannian setting.

Contribution

It introduces a sub-Riemannian analog of the classical area formula specifically for Lipschitz mappings in equiregular Carnot--Carathéodory spaces, a significant extension of geometric measure theory.

Findings

Proves the sub-Riemannian area formula for Lipschitz maps

Extends classical area formula to Carnot--Carathéodory spaces

Provides tools for geometric analysis in sub-Riemannian geometry

Abstract

We prove the sub-Riemannian analog of the area formula for Lipschitz (in sub-Riemannian sense) mappings of equiregular Carnot--Carath\'{e}odory spaces.