Work

Constructing diffeomorphisms and homeomorphisms with prescribed derivative

Year: 2024

Type: article

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 $\varepsilon$. 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.

Source: Advances in Mathematics

DOI: 10.1016/j.aim.2024.110020

Authors: Paweł Goldstein, Zofia Grochulska, Piotr Hajłasz

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,510