Lipschitz Functions on Submanifolds of Heisenberg Groups
Abstract
We study the behavior of Lipschitz functions on intrinsic C1 submanifolds of Heisenberg groups: our main result is their almost everywhere tangential Pansu differentiability. We also provide two applications: a Lusin-type approximation of Lipschitz functions on H-rectifiable sets and a coarea formula on H-rectifiable sets that completes the program started in [18].
Main Authors
Format
Articles
Research article
Published
2023
Series
Subjects
Publication in research information system
Publisher
Oxford University Press (OUP)
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202210244961Use this for linking
Review status
Peer reviewed
ISSN
1073-7928
DOI
https://doi.org/10.1093/imrn/rnac066
Language
English
Published in
International Mathematics Research Notices
Citation
- Julia, A., Nicolussi Golo, S., & Vittone, D. (2023). Lipschitz Functions on Submanifolds of Heisenberg Groups. International Mathematics Research Notices, 2023(9), 7399-7422. https://doi.org/10.1093/imrn/rnac066
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Funder(s)
Research Council of Finland
Funding program(s)
Academy Project, AoF
Akatemiahanke, SA
Additional information about funding
This work was supported by University of Padova STARS Project “Sub-Riemannian Geometry and Geometric Measure Theory Issues: Old and New”; the Simons Foundation [grant 601941 to A. J.]; the Academy of Finland [grants 322898 “Sub-Riemannian Geometry via Metric-geometry and Lie-group Theory” and 314172 “Quantitative rectifiability in Euclidean and non-Euclidean spaces” to S. N. G.]; FFABR 2017 of MIUR (Italy); and GNAMPA of INdAM (Italy) to [D. V.].
Copyright© The Author(s) 2022. Published by Oxford University Press.