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arXiv · 2004.02520

Area of intrinsic graphs and coarea formula in Carnot Groups

Antoine Julia·Sebastiano Nicolussi Golo·Davide Vittone
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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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Antoine Julia, Sebastiano Nicolussi Golo, Davide Vittone. 2020-04-06. Area of intrinsic graphs and coarea formula in Carnot Groups. https://arxiv.org/abs/2004.02520

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