English

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 C1C^1 regularity (CH1C^1_H). Our first main result is an area formula for CH1C^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 CH1C^1_H submanifolds into level sets of a CH1C^1_H 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}
}