A1 Journal article (refereed)
Two‐dimensional metric spheres from gluing hemispheres (2022)

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

JYU authors or editors

Ikonen, Toni

Publication details

All authors or editors: Ikonen, Toni

Journal or series: Journal of the London Mathematical Society

ISSN: 0024-6107

eISSN: 1469-7750

Publication year: 2022

Publication date: 20/06/2022

Volume: 106

Issue number: 4

Pages range: 3069-3102

Publisher: Wiley-Blackwell

Publication country: United Kingdom

Publication language: English

DOI: https://doi.org/10.1112/jlms.12656

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/82087

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2106.01295

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.

Keywords: complex analysis; measure theory; geometry; metric spaces

Fields of science: