Quasiconformally Bi-Homogeneous Compacta in the Complex Plane

MacManus, Paul; Näkki, Raimo; Palka, Bruce

doi:10.1112/s0024611599001690

Cited by 11 publications

(20 citation statements)

References 16 publications

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“…The concept of quasiconformal homogeneity was introduced and developed by Gehring and Palka in [7]; for other work on quasiconformally homogeneous structures see [8], [9], [4], and [5]. In dimensions three and above, owing to well-known quasiconformal rigidity phenomena, the property of being uniformally quasiconformally homogeneous is a topologically restrictive one, we recall Theorem 1.3 of [4].…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

Teichmuller Mappings, Quasiconformal Homogeneity, and Non-amenable Covers of Riemann Surfaces

Bonfert-Taylor

Martin

Reid³

et al. 2011

Pure and Applied Mathematics Quarterly

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We show that there exists a universal constant K c so that every K-strongly quasiconformally homogeneous hyperbolic surface X (not equal to H 2 ) has the property that K > K c > 1. The constant K c is the best possible, and is computed in terms of the diameter of the (2, 3, 7)-hyperbolic orbifold (which is the hyperbolic orbifold of smallest area.) We further show that the minimum strong homogeneity constant of a hyperbolic surface without conformal automorphisms decreases if one passes to a non-amenable regular cover.

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Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

Teichmuller Mappings, Quasiconformal Homogeneity, and Non-amenable Covers of Riemann Surfaces

Bonfert-Taylor

Martin

Reid³

et al. 2011

Pure and Applied Mathematics Quarterly

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“…However, they show that the middle- MacManus, Näkki, and Palka [24] further define a subset E ⊂ C to be uniformly quasiconformally bi-homogeneous if there exists…”

Section: Quasiconformally Homogeneous Subsets Of R Nmentioning

confidence: 99%

Quasiconformal Homogeneity after Gehring and Palka

Bonfert-Taylor

Canary

Taylor

2014

Comput. Methods Funct. Theory

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“…The study of the quasiconformal homogeneity properties of planar sets was begun by Gehring and Palka in [6] (see also [8] and [9].) Let M be a uniformly quasiconformally homogenous hyperbolic manifold.…”

Section: Basic Factsmentioning

confidence: 99%

Quasiconformal homogeneity of hyperbolic surfaces with fixed-point full automorphisms

Bonfert-Taylor¹,

Bridgeman²,

Canary³

et al. 2007

Math. Proc. Camb. Phil. Soc.

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Abstract. We show that any closed hyperbolic surface admitting a conformal automorphism with "many" fixed points is uniformly quasiconformally homogeneous, with constant uniformly bounded away from 1. In particular, there is a uniform lower bound on the quasiconformal homogeneity constant for all hyperelliptic surfaces. In addition, we introduce more restrictive notions of quasiconformal homogeneity and bound the associated quasiconformal homogeneity constants uniformly away from 1 for all hyperbolic surfaces.

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Quasiconformally Bi-Homogeneous Compacta in the Complex Plane

Cited by 11 publications

References 16 publications

Teichmuller Mappings, Quasiconformal Homogeneity, and Non-amenable Covers of Riemann Surfaces

Teichmuller Mappings, Quasiconformal Homogeneity, and Non-amenable Covers of Riemann Surfaces

Quasiconformal Homogeneity after Gehring and Palka

Quasiconformal homogeneity of hyperbolic surfaces with fixed-point full automorphisms

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