Universität zu Köln

Ikonen, Toni ORCID: 0000-0001-5969-7912 and Romney, Matthew (2022). Quasiconformal geometry and removable sets for conformal mappings. J. Anal. Math., 148 (1). S. 119 - 186. JERUSALEM: HEBREW UNIV MAGNES PRESS. ISSN 1565-8538

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Abstract

We study metric spaces defined via a conformal weight, or more generally a measurable Finsler structure, on a domain omega subset of Double-struck capital R-2 that vanishes on a compact set E subset of omega 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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Ikonen, Toni UNSPECIFIED orcid.org/0000-0001-5969-7912 UNSPECIFIED Romney, Matthew UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-667287
DOI:	10.1007/s11854-022-0224-5
Journal or Publication Title:	J. Anal. Math.
Volume:	148
Number:	1
Page Range:	S. 119 - 186
Date:	2022
Publisher:	HEBREW UNIV MAGNES PRESS
Place of Publication:	JERUSALEM
ISSN:	1565-8538
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language PARAMETERIZATIONS; UNIFORMIZATION; DISTANCE; MODULUS Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/66728