A1 Journal article (refereed)
Abstract and concrete tangent modules on Lipschitz differentiability spaces (2022)

Ikonen, T., Pasqualetto, E., & Soultanis, E. (2022). Abstract and concrete tangent modules on Lipschitz differentiability spaces. Proceedings of the American Mathematical Society, 150(1), 327-343. https://doi.org/10.1090/proc/15656

JYU authors or editors

Publication details

All authors or editorsIkonen, Toni; Pasqualetto, Enrico; Soultanis, Elefterios

Journal or seriesProceedings of the American Mathematical Society



Publication year2022

Publication date19/10/2021


Issue number1

Pages range327-343

PublisherAmerican Mathematical Society (AMS)

Publication countryUnited States

Publication languageEnglish


Publication open accessNot open

Publication channel open access

Publication is parallel published (JYX)https://jyx.jyu.fi/handle/123456789/78616

Publication is parallel publishedhttps://arxiv.org/abs/2011.15092


We construct an isometric embedding from Gigli’s abstract tangent module into the concrete tangent module of a space admitting a (weak) Lipschitz differentiable structure, and give two equivalent conditions which characterize when the embedding is an isomorphism. Together with arguments from Bate, Kangasniemi, and Orponen, Cheeger’s differentiation theorem via the multilinear Kakeya inequality, arXiv:1904.00808 (2019), this equivalence is used to show that the –-type condition self-improves to .

We also provide a direct proof of a result by Gigli and Pasqualetto, Equivalence of two different notions of tangent bundle on rectifiable metric measure spaces, arXiv:1611.09645 that, for a space with a strongly rectifiable decomposition, Gigli’s tangent module admits an isometric embedding into the so-called Gromov–Hausdorff tangent module, without any a priori reflexivity assumptions.

Keywordsmathematicsmetric spacesequivalence

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Reporting Year2022

JUFO rating2

Last updated on 2024-22-04 at 16:50