Bi-Lipschitz homogeneous curves in ℝ² are quasicircles

DOI10.1090/S0002-9947-01-02755-6zbMath0979.30012MaRDI QIDQ2719039

Christopher J. Bishop

Publication date: 14 May 2001

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Hausdorff dimensionquasiconformal mappingsquasicirclesbounded turningbi-Lipschitz mappingschord-archomogeneous continuaquasihomogeneous embeddings

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65)

Related Items (8)

Möbius bilipschitz homogeneous arcs on the plane ⋮ Inversion invariant bilipschitz homogeneity ⋮ Bilipschitz homogeneity and inner diameter distance ⋮ Lipschitz means and mixers on metric spaces ⋮ Doubling property for bilipschitz homogeneous geodesic surfaces ⋮ Bilipschitz homogeneous Jordan curves, Möbius maps, and dimension ⋮ Geodesic manifolds with a transitive subset of smooth biLipschitz maps ⋮ Bi-Lipschitz maps in \(Q\)-regular Loewner spaces

Cites Work

• Classifying homogeneous continua
• Quasiconformally homogeneous curves
• Higher dimensional Ahlfors regular sets and chordarc curves in \(R^n\)
• Bilipschitz group actions and homogeneous Jordan curves
• Quasiconformally homogeneous compacta in the complex plane
• Trajectories of one-parameters groups of quasi-isometries
• A homogeneous indecomposable plane continuum
• On Lipschitz Homogeneity of the Hilbert Cube
• Quasiconformally Bi-Homogeneous Compacta in the Complex Plane
• Quasisymmetric embeddings of metric spaces
• On topologically and quasiconformally homogeneous continua
• Bilipschitz homogeneous Jordan curves
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