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


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Publication details

All authors or editorsIkonen, Toni; Romney, Matthew

Journal or seriesJournal d'Analyse Mathématique

ISSN0021-7670

eISSN1565-8538

Publication year2022

Publication date25/08/2022

Volume148

Issue number1

Pages range119-185

PublisherHebrew University Magnes Press; Springer

Publication countryIsrael

Publication languageEnglish

DOIhttps://doi.org/10.1007/s11854-022-0224-5

Publication open accessNot open

Publication channel open access

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

Publication is parallel publishedhttps://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.


Keywordsgeometrymetric spacescomplex analysis


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Ministry reportingYes

Reporting Year2022

JUFO rating2


Last updated on 2024-03-04 at 21:46