Mappings of Finite Distortion : Compactness of the Branch Set
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.
Main Authors
Format
Articles
Research article
Published
2021
Series
Subjects
Publication in research information system
Publisher
Hebrew University Magnes Press; Springer
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202110045052Use this for linking
Review status
Peer reviewed
ISSN
0021-7670
DOI
https://doi.org/10.1007/s11854-021-0153-8
Language
English
Published in
Journal d'Analyse Mathematique
Citation
- 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
License
Funder(s)
Research Council of Finland
Research Council of Finland
Funding program(s)
Postdoctoral Researcher, AoF
Academy Project, AoF
Tutkijatohtori, SA
Akatemiahanke, SA
Additional information about funding
A. K. acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the “María de Maeztu” Programme for Units of Excellence in R&D (MDM-2014-0445) and MTM-2016-77635-P (MICINN, Spain) and Academy of Finland project 322441.
R. L. was supported by the Finnish Academy of Science and Letters.
V. T. was supported by the Academy of Finland Projects 277923 and 308759.
Copyright© 2021 The Hebrew University of Jerusalem