A1 Journal article (refereed)
Universal Infinitesimal Hilbertianity of Sub-Riemannian Manifolds (2023)

Le Donne, E., Lučić, D., & Pasqualetto, E. (2023). Universal Infinitesimal Hilbertianity of Sub-Riemannian Manifolds. Potential Analysis, 59(1), 349-374. https://doi.org/10.1007/s11118-021-09971-8

JYU authors or editors

Publication details

All authors or editors: Le Donne, Enrico; Lučić, Danka; Pasqualetto, Enrico

Journal or series: Potential Analysis

ISSN: 0926-2601

eISSN: 1572-929X

Publication year: 2023

Publication date: 11/04/2022

Volume: 59

Issue number: 1

Pages range: 349-374

Publisher: Springer

Publication country: Netherlands

Publication language: English

DOI: https://doi.org/10.1007/s11118-021-09971-8

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/80582

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1910.05962

Abstract

We prove that sub-Riemannian manifolds are infinitesimally Hilbertian (i.e., the associated Sobolev space is Hilbert) when equipped with an arbitrary Radon measure. The result follows from an embedding of metric derivations into the space of square-integrable sections of the horizontal bundle, which we obtain on all weighted sub-Finsler manifolds. As an intermediate tool, of independent interest, we show that any sub-Finsler distance can be monotonically approximated from below by Finsler ones. All the results are obtained in the general setting of possibly rank-varying structures.

Keywords: differential geometry; functional analysis; manifolds (mathematics); Riemannian manifolds

Free keywords: infinitesimal hilbertianity; Sobolev space; sub-Riemannian manifold; sub-Finsler manifold

Contributing organizations

Related projects

Ministry reporting: Yes

Reporting Year: 2022

JUFO rating: 2