Displaying similar documents to “Characterizations of quasidisks”

What is a disk?

Kari Hag (1999)

Banach Center Publications

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This paper should be considered as a companion report to F.W. Gehring’s survey lectures “Characterizations of quasidisks” given at this Summer School [7]. Notation, definitions and background results are given in that paper. In particular, D is a simply connected proper subdomain of R 2 unless otherwise stated and D* denotes the exterior of D in R ¯ 2 . Many of the characterizations of quasidisks have been motivated by looking at properties of euclidean disks. It is therefore natural to go...

Hilbert-Smith Conjecture for K - Quasiconformal Groups

Gong, Jianhua (2010)

Fractional Calculus and Applied Analysis

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MSC 2010: 30C60 A more general version of Hilbert's fifth problem, called the Hilbert-Smith conjecture, asserts that among all locally compact topological groups only Lie groups can act effectively on finite-dimensional manifolds. We give a solution of the Hilbert-Smith Conjecture for K - quasiconformal groups acting on domains in the extended n - dimensional Euclidean space.

Quasiconformal mappings onto John domains.

Juha Heinonen (1989)

Revista Matemática Iberoamericana

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In this paper we study quasiconformal homeomorphisms of the unit ball B = B = {x ∈ R: |x| < 1} of R onto John domains. We recall that John domains were introduced by F. John in his study of rigidity of local quasi-isometries [J]; the term John domain was coined by O. Martio and J. Sarvas seventeen years later [MS]. From the various equivalent characterizations we shall adapt the following definition based on diameter carrots, cf. [V4], [V5], [NV].