Area of intrinsic graphs and coarea formula in Carnot groups
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.
Main Authors
Format
Articles
Research article
Published
2022
Series
Subjects
Publication in research information system
Publisher
Springer Science and Business Media LLC
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202202171547Use this for linking
Review status
Peer reviewed
ISSN
0025-5874
DOI
https://doi.org/10.1007/s00209-021-02916-2
Language
English
Published in
Mathematische Zeitschrift
Citation
- 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
Additional information about funding
The authors are supported by the University of Padova STARS Project “Sub-Riemannian Geometry and
Geometric Measure Theory Issues: Old and New” (SUGGESTION). They also acknowledge the support of
GNAMPA of INdAM and FFABR 2017 of MIUR (Italy). Open Access funding provided by University of Jyväskylä (JYU).
Copyright© The Author(s) 2022