Bilipschitz homogeneity and inner diameter distance

We prove that a Jordan plane domain whose boundary is bilipschitz homogeneous with respect to its inner diameter distance is a John disk. This opens the door to an abundance of equivalent conditions. We characterize such domains in terms of quasiconformal mappings as well as their Riemann maps. We i...

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Bibliographic Details
Published in:Journal d'analyse mathématique (Jerusalem) 2010-05, Vol.111 (1), p.1-46
Main Authors: Freeman, David M., Herron, David A.
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Analysis
Dynamical Systems and Ergodic Theory
Functional Analysis
Mathematics
Mathematics and Statistics
Partial Differential Equations
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Summary:We prove that a Jordan plane domain whose boundary is bilipschitz homogeneous with respect to its inner diameter distance is a John disk. This opens the door to an abundance of equivalent conditions. We characterize such domains in terms of quasiconformal mappings as well as their Riemann maps. We introduce the notion of an inner diameter distance Jordan disk and present related results for these spaces.
ISSN:0021-7670
1565-8538
DOI:10.1007/s11854-010-0011-6