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

Ikonen, Toni

Publication details

All authors or editors: Ikonen, Toni; Pasqualetto, Enrico; Soultanis, Elefterios

Journal or series: Proceedings of the American Mathematical Society

ISSN: 0002-9939

eISSN: 1088-6826

Publication year: 2022

Publication date: 19/10/2021

Volume: 150

Issue number: 1

Pages range: 327-343

Publisher: American Mathematical Society (AMS)

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1090/proc/15656

Publication open access: Not open

Publication channel open access:

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

Publication is parallel published: https://arxiv.org/abs/2011.15092

Abstract

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.

Keywords: mathematics; metric spaces; equivalence

Fields of science: