Extending homeomorphisms of the circle to quasiconformal homeomorphisms of the disk
نویسندگان
چکیده
منابع مشابه
On Boundary Homeomorphisms of Trans-quasiconformal Maps of the Disk
This paper studies boundary homeomorphisms of trans-quasiconformal maps of the unit disk. Motivated by Beurling-Ahlfors’s well-known quasisymmetry condition, we introduce the “scalewise” and “pointwise” distortions of a circle homeomorphism and formulate conditions in terms of each that guarantee the existence of a David extension to the disk. These constructions are also used to obtain extensi...
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An analogous theorem holds for quasi-conformal homeomorphisms between subdomains of S, as can easily be seen from the fact that all of the above statements are local in nature. Here a.e. refers to the Lebesgue measure on S. Throughout these notes, all measures will be Borel measures on the appropriate topological space, which will always be some Borel subset of R for some n. ”Almost everywhere”...
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Homeomorphisms of the circle were first considered by Poincare* who used them to obtain qualitative results for a class of differential equations on the torus. He classified those which have a dense orbit by showing that they are topologically equivalent to a rotation through an angle incommensurable with IT. However, Denjoy showed that there exist homeomorphisms of the circle without periodic ...
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Let Hg be a genus g handlebody and MCG2n(Tg) be the group of the isotopy classes of orientation preserving homeomorphisms of Tg = ∂Hg, fixing a given set of 2n points. In this paper we find a finite set of generators for E 2n, the subgroup of MCG2n(Tg) consisting of the isotopy classes of homeomorphisms of Tg admitting an extension to the handlebody and keeping fixed the union of n disjoint pro...
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We introduce and study the notion of a chain group of homeomorphisms of a one-manifold, which is a certain generalization of Thompson’s group F. Precisely, this is a group finitely generated by homeomorphisms, each supported on exactly one interval in a chain, and subject to a certain mild dynamical condition. The resulting class of groups exhibits a combination of uniformity and diversity. On ...
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ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2007
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2007.11.517