A1 Journal article (refereed)
Quasiconformal geometry and removable sets for conformal mappings (2022)

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

JYU authors or editors

Publication details

All authors or editors: Ikonen, Toni; Romney, Matthew

Journal or series: Journal d'Analyse Mathématique

ISSN: 0021-7670

eISSN: 1565-8538

Publication year: 2022

Publication date: 25/08/2022

Volume: 148

Issue number: 1

Pages range: 119-185

Publisher: Hebrew University Magnes Press; Springer

Publication country: Israel

Publication language: English

DOI: https://doi.org/10.1007/s11854-022-0224-5

Publication open access: Not open

Publication channel open access:

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/82857

Publication is parallel published: https://arxiv.org/abs/2006.02776

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.

Keywords: geometry; metric spaces; complex analysis

Contributing organizations

Related projects

Ministry reporting: Yes

Reporting Year: 2022

Preliminary JUFO rating: 2