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On quasiconformal equivalence of Schottky regions

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arxiv 2306.06469 v2 pith:PFZUUOVT submitted 2023-06-10 math.CV

Ruben A. Hidalgo This is my paper · ORCID
classification math.CV
keywords regionsschottkydiscontinuityequivalencegroupsalternativeapproachdiscuss
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In a recent paper, H. Shiga proved that the regions of discontinuity of any two Schottky groups of ranks at least two are quasiconformally equivalent. In this paper, we provide an alternative proof of such a fact. Our approach permits us to discuss quasiconformality equivalence of regions of discontinuity of Schottky type groups in terms of their signatures.

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  1. Quasisymmetric universality, quasi-isometric classification and topological rigidity of Kleinian groups

    math.GT 2026-08 conditional novelty 8.0 of 10

    The quasisymmetric, quasiconformal, and quasi-isometric classification of geometrically finite Kleinian group limit sets is governed by the absence of Sierpiński carpet subsets and by the homogeneity of rank-two cut points.

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