Calculus of Variations and Geometric Measure Theory

A. Julia - S. Nicolussi Golo - D. Vittone

Area of intrinsic graphs and coarea formula in Carnot Groups

created by nicolussigolo on 08 Apr 2020
modified by vittone on 24 Mar 2022


Published Paper

Inserted: 8 apr 2020
Last Updated: 24 mar 2022

Journal: Math. Z.
Year: 2022

ArXiv: 2004.02520 PDF


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.