A1 Journal article (refereed)
Area of intrinsic graphs and coarea formula in Carnot groups (2022)

Julia, A., Nicolussi Golo, S., & Vittone, D. (2022). Area of intrinsic graphs and coarea formula in Carnot groups. Mathematische Zeitschrift, 301(2), 1369-1406. https://doi.org/10.1007/s00209-021-02916-2

JYU authors or editors

Publication details

All authors or editors: Julia, Antoine; Nicolussi Golo, Sebastiano; Vittone, Davide

Journal or series: Mathematische Zeitschrift

ISSN: 0025-5874

eISSN: 1432-1823

Publication year: 2022

Publication date: 18/01/2022

Volume: 301

Issue number: 2

Pages range: 1369-1406

Publisher: Springer Science and Business Media LLC

Publication country: Germany

Publication language: English

DOI: https://doi.org/10.1007/s00209-021-02916-2

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/79820

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2004.02520

Abstract

We consider submanifolds of sub-Riemannian Carnot groups with intrinsic C1 regularity (C1H). Our first main result is an area formula for C1H 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 C1H submanifolds into level sets of a C1H function.

Keywords: differential geometry; measure theory; group theory

Free keywords: Carnot groups; area formula; coarea formula; Hausdorff measures; submanifolds

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2022

JUFO rating: 2