A1 Journal article (refereed)
Fibers of Monotone Maps of Finite Distortion (2022)

Kangasniemi, I., & Onninen, J. (2022). Fibers of Monotone Maps of Finite Distortion. Journal of Geometric Analysis, 32(12), Article 299. https://doi.org/10.1007/s12220-022-01038-3

JYU authors or editors

Publication details

All authors or editors: Kangasniemi, Ilmari; Onninen, Jani

Journal or series: Journal of Geometric Analysis

ISSN: 1050-6926

eISSN: 1559-002X

Publication year: 2022

Publication date: 23/09/2022

Volume: 32

Issue number: 12

Article number: 299

Publisher: Springer

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1007/s12220-022-01038-3

Publication open access: Not open

Publication channel open access: 

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2201.03995

Abstract

We study topologically monotone surjective W1,n-maps of finite distortion f:Ω→Ω′, where Ω,Ω′ are domains in Rn, n≥2. If the outer distortion function Kf∈Lploc(Ω) with p≥n−1, then any such map f is known to be homeomorphic, and hence the fibers f−1{y} are singletons. We show that as the exponent of integrability p of the distortion function Kf increases in the range 1/(n−1)≤p0.

Keywords: complex analysis; partial differential equations; cohomology

Free keywords: mappings of finite distortion; MFD; monotone; fiber; homology; conformal cohomology

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2022

JUFO rating: 2