A1 Journal article (refereed)
Constructing diffeomorphisms and homeomorphisms with prescribed derivative (2025)

Goldstein, P., Grochulska, Z., & Hajłasz, P. (2025). Constructing diffeomorphisms and homeomorphisms with prescribed derivative. Advances in Mathematics, 460, Article 110020. https://doi.org/10.1016/j.aim.2024.110020

JYU authors or editors

Publication details

All authors or editors: Goldstein, Paweł; Grochulska, Zofia; Hajłasz, Piotr

Journal or series: Advances in Mathematics

ISSN: 0001-8708

eISSN: 1090-2082

Publication year: 2025

Publication date: 22/11/2024

Volume: 460

Article number: 110020

Publisher: Elsevier

Publication country: Belgium

Publication language: English

DOI: https://doi.org/10.1016/j.aim.2024.110020

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/98640

Web address of parallel published publication (pre-print):  https://doi.org/10.48550/arXiv.2312.13078

Abstract

We prove that for any measurable mapping T into the space of matrices with positive determinant, there is a diffeomorphism whose derivative equals T outside a set of measure less than ε. We use this fact to prove that for any measurable mapping T into the space of matrices with non-zero determinant (with no sign restriction), there is an almost everywhere approximately differentiable homeomorphism whose derivative equals T almost everywhere.

Keywords: measure theory; differential calculus

Free keywords: approximate differentiability; homeomorphisms; drescribed derivative

Contributing organizations

Ministry reporting: Yes

VIRTA submission year: 2025

Preliminary JUFO rating: 3