Abstract
We study metric spaces defined via a conformal weight, or more generally a measurable Finsler structure, on a domain Ω ⊂ ℝ2 that vanishes on a compact set E ⊂ Ω 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.
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Both authors were supported by the Academy of Finland, project number 308659. The first author was also supported by the Vilho, Yrjö and Kalle Väisälä Foundation. The second author was also supported by Deutsche Forschungsgemeinschaft grant SPP 2026.
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Ikonen, T., Romney, M. Quasiconformal geometry and removable sets for conformal mappings. JAMA 148, 119–185 (2022). https://doi.org/10.1007/s11854-022-0224-5
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DOI: https://doi.org/10.1007/s11854-022-0224-5