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- W2046335770 abstract "We call the complement of a union of at least three disjoint (round)open balls in the unit sphere ${Bbb S}^n$ a Schottky set. We prove that every quasisymmetric homeomorphism of a Schottky set ofspherical measure zero to another Schottky set is the restrictionof a Mobius transformation on ${Bbb S}^n$. In the other direction weshow that every Schottky set in ${Bbb S}^2$ of positive measure admits nontrivial quasisymmetric maps to other Schottky sets. These resultsare applied to establish rigidity statements for convex subsets ofhyperbolic space that have totally geodesic boundaries." @default.
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- W2046335770 date "2009-01-01" @default.
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- W2046335770 title "Rigidity of Schottky sets" @default.
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- W2046335770 doi "https://doi.org/10.1353/ajm.0.0045" @default.
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