Calculus of Variations and Geometric Measure Theory
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A. Julia - S. Nicolussi Golo - D. Vittone

Area of intrinsic graphs and coarea formula in Carnot Groups

created by nicolussigolo on 08 Apr 2020

[BibTeX]

preprint

Inserted: 8 apr 2020

Year: 2020

ArXiv: 2004.02520 PDF

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.

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