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