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