Abstract
AbstractWe establish nine equivalent conditions for a bounded domain which is quasiconformally equivalent to a bounded uniform domain with a connected boundary to be a John domain. These conditions connect the John property of the domain with other geometric properties, and with the quasisymmetry of quasiconformal mappings onto it. Our result is a generalization of the main result of Heinonen (Rev. Math. Iber. 5: 97–123, 1989), where a similar question was studied in the special case of the unit ball.
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