Published Paper

Inserted: 8 apr 2020
Last Updated: 24 mar 2022

Journal: Math. Z.
Year: 2022
Doi: https://doi.org/10.1007/s00209-021-02916-2

Abstract:

We consider submanifolds of sub-Riemannian Carnot groups with intrinsic $C^1$ regularity ($C^1_H$). Our first main result is an area formula for $C^1_H$ intrinsic graphs; as an application, we deduce density properties for Hausdorff measures on rectifiable sets. Our second main result is a coarea formula for slicing $C^1_H$ submanifolds into level sets of a $C^1_H$ function.