A1 Journal article (refereed)
Mappings of Finite Distortion : Compactness of the Branch Set (2021)

Kauranen, A., Luisto, R., & Tengvall, V. (2021). Mappings of Finite Distortion : Compactness of the Branch Set. Journal d'Analyse Mathematique, 143(1), 207-229. https://doi.org/10.1007/s11854-021-0153-8

JYU authors or editors

Publication details

All authors or editors: Kauranen, Aapo; Luisto, Rami; Tengvall, Ville

Journal or series: Journal d'Analyse Mathematique

ISSN: 0021-7670

eISSN: 1565-8538

Publication year: 2021

Publication date: 07/05/2021

Volume: 143

Issue number: 1

Pages range: 207-229

Publisher: Hebrew University Magnes Press; Springer

Publication country: Israel

Publication language: English

DOI: https://doi.org/10.1007/s11854-021-0153-8

Publication open access: Not open

Publication channel open access: Channel is not openly available

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/77994

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1709.08724

Additional information: Preprint myös JYXissä: https://jyx.jyu.fi/handle/123456789/58809

Abstract

We show that an entire branched cover of finite distortion cannot have a compact branch set if its distortion satisfies a certain asymptotic growth condition. We furthermore show that this bound is strict by constructing an entire, continuous, open and discrete mapping of finite distortion which is piecewise smooth, has a branch set homeomorphic to an (n − 2)-dimensional torus and distortion arbitrarily close to the asymptotic bound.

Keywords: complex analysis; topology; manifolds (mathematics)

Free keywords: finite distortion; branch sets

Contributing organizations

Related projects

Ministry reporting: Yes

Reporting Year: 2021

JUFO rating: 2