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 editorsLe Donne, Enrico; Lučić, Danka; Pasqualetto, Enrico

Journal or seriesPotential Analysis



Publication year2023

Publication date11/04/2022


Issue number1

Pages range349-374


Publication countryNetherlands

Publication languageEnglish


Publication open accessOpenly available

Publication channel open accessPartially 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


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.

Keywordsdifferential geometryfunctional analysismanifolds (mathematics)Riemannian manifolds

Free keywordsinfinitesimal hilbertianity; Sobolev space; sub-Riemannian manifold; sub-Finsler manifold

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Ministry reportingYes

Reporting Year2022

JUFO rating2

Last updated on 2024-15-06 at 22:26