Two‐dimensional metric spheres from gluing hemispheres
Abstract
We study metric spheres (Z,dZ) obtained by gluing two hemispheres of S2 along an orientation-preserving homeomorphism g:S1→S1, where dZ is the canonical distance that is locally isometric to S2 off the seam. We show that if (Z,dZ) is quasiconformally equivalent to S2, in the geometric sense, then g is a welding homeomorphism with conformally removable welding curves. We also show that g is bi-Lipschitz if and only if (Z,dZ) has a 1-quasiconformal parametrization whose Jacobian is comparable to the Jacobian of a quasiconformal mapping h:S2→S2. Furthermore, we show that if g−1 is absolutely continuous and g admits a homeomorphic extension with exponentially integrable distortion, then (Z,dZ) is quasiconformally equivalent to S2.
Main Author
Format
Articles
Research article
Published
2022
Series
Subjects
Publication in research information system
Publisher
Wiley-Blackwell
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202206293687Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
0024-6107
DOI
https://doi.org/10.1112/jlms.12656
Language
English
Published in
Journal of the London Mathematical Society
Citation
- Ikonen, T. (2022). Two‐dimensional metric spheres from gluing hemispheres. Journal of the London Mathematical Society, 106(4), 3069-3102. https://doi.org/10.1112/jlms.12656
License
Funder(s)
Research Council of Finland
Funding program(s)
Academy Project, AoF
Akatemiahanke, SA
Additional information about funding
Academy of Finland, Grant/AwardNumber: 308659;
Vilho, Yrjö and Kalle Väisälä Foundation
Copyright© 2022 the Authors