Quasiconformal geometry and removable sets for conformal mappings
Abstract
We study metric spaces defined via a conformal weight, or more generally a measurable Finsler structure, on a domain Ω ⊂ ℝ2 that vanishes on a compact set E ⊂ Ω and satisfies mild assumptions. Our main question is to determine when such a space is quasiconformally equivalent to a planar domain. We give a characterization in terms of the notion of planar sets that are removable for conformal mappings. We also study the question of when a quasiconformal mapping can be factored as a 1-quasiconformal mapping precomposed with a bi-Lipschitz map.
Main Authors
Format
Articles
Research article
Published
2022
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-202208294386Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
0021-7670
DOI
https://doi.org/10.1007/s11854-022-0224-5
Language
English
Published in
Journal d'Analyse Mathématique
Citation
- Ikonen, T., & Romney, M. (2022). Quasiconformal geometry and removable sets for conformal mappings. Journal d'Analyse Mathématique, 148(1), 119-185. https://doi.org/10.1007/s11854-022-0224-5
License
Funder(s)
Research Council of Finland
Funding program(s)
Academy Project, AoF
Akatemiahanke, SA
Additional information about funding
Both authors were supported by the Academy of Finland, project number 308659. The first author was also supported by the Vilho, Yrjö and Kalle Väisälä Foundation. The second author was also supported by Deutsche Forschungsgemeinschaft grant SPP 2026.
Copyright© 2022, The Hebrew University of Jerusalem