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Đề tài " Quasiconformal homeomorphisms and the convex hull boundary "
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We investigate the relationship between an open simply-connected region Ω ⊂ S2 and the boundary Y of the hyperbolic convex hull in H3 of S2 \ Ω. A counterexample is given to Thurston’s conjecture that these spaces are related by a 2-quasiconformal homeomorphism which extends to the identity map on their common boundary, in the case when the homeomorphism is required to respect any group of M¨bius transformations which preserves Ω.
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