Two‐dimensional metric spheres from gluing hemispheres
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
Published inJournal of the London Mathematical Society
© 2022 the Authors
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.
ISSN Search the Publication Forum0024-6107
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Related funder(s)Academy of Finland
Funding program(s)Academy Project, AoF
Additional information about fundingAcademy of Finland, Grant/AwardNumber: 308659; Vilho, Yrjö and Kalle Väisälä Foundation
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