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Generalized Angles in Ptolemaic Möbius Structures. II
We continue studying the BAD class of multivalued map**s of Ptolemaic Möbius structures in the sense of Buyalo with controlled distortion of...
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Free distance ratio map**s in Banach spaces
In this paper, we introduce a class of map**s related to the distance ratio metric and study its connection to the freely quasiconformal map** in...
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A remark on quasimöbius and quasiconformal maps
The main purpose of this note is to show a certain connection between quasiconformal and quasimöbius maps. We prove that quasimöbius maps are the...
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Generalized Angles in Ptolemaic Möbius Structures
We show that each Ptolemaic semimetric is Möbius-equivalent to a bounded metric. Introducing generalized angles in Ptolemaic Möbius structures, we...
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Möbius bilipschitz homogeneous arcs on the plane
A möbius bilipschitz map** is an η-quasimöbius map** with the linear distortion function η( t ) = Kt . We show that if an open Jordan arc γ ⊂ C with...
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An extendability condition for bilipschitz functions
We give a new definition of λ-relatively connected set, some generalization of a uniformly perfect set. This definition is equivalent to the old...
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Quasi-Conformal Map**s
In this chapter, we first give a brief overview of the classical theory of quasiconformal map**s in the complex plane and then we explain how to...
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Locally Quasi-Möbius Map**s on a Circle
We introduce the notion of a
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The quasimöbius property on small circles and quasiconformality
We prove that every map**, without requiring its injectivity or continuity, of a domain of the extended plane which is ω -quasimöbius on...
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Map**s slightly changing a fixed cross-ratio
Given a complex number λ ≠ 0, 1, we consider local homeomorphisms of a domain D ⊂ ℂ̄ that, in a neighborhood of every point, change slightly (with a...
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The Möbius midpoint condition as a test for quasiconformality and the quasimöbius property
The Möbius midpoint condition, introduced by Goldberg in 1974 as a criterion for the quasisymmetry of a map** of the line onto itself and...
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