Area of intrinsic graphs and coarea formula in Carnot Groups
Classical Analysis and ODEs
2020-04-07 v1 Differential Geometry
Metric Geometry
Abstract
We consider submanifolds of sub-Riemannian Carnot groups with intrinsic regularity (). Our first main result is an area formula for 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 submanifolds into level sets of a function.
Keywords
Cite
@article{arxiv.2004.02520,
title = {Area of intrinsic graphs and coarea formula in Carnot Groups},
author = {Antoine Julia and Sebastiano Nicolussi Golo and Davide Vittone},
journal= {arXiv preprint arXiv:2004.02520},
year = {2020}
}