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

Publication details

All authors or editorsIkonen, Toni

Journal or seriesJournal of the London Mathematical Society



Publication year2022

Publication date20/06/2022


Issue number4

Pages range3069-3102


Publication countryUnited Kingdom

Publication languageEnglish


Publication open accessOpenly available

Publication channel open accessPartially 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


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.

Keywordscomplex analysismeasure theorygeometrymetric spaces

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Ministry reportingYes

Reporting Year2022

JUFO rating2

Last updated on 2024-03-04 at 19:37