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Diffeomorphic approximation of quasiconformal and quasisymmetric homeomorphisms. (English) Zbl 0565.30015

Continuing the study of J. Luukkainen and P. Tukia [ibid. 6, 343-367 (1981; Zbl 0456.57005)] on piecewise linear approximation for quasisymmetric embeddings and also his own [Ann. Acad. Sci. Fenn., Ser. A I, Diss. 30, 24 p. (1980; Zbl 0421.57005)] for quasiconformal and bilipschitzian homeomorphisms, the author obtains their \(C^{\infty}\)- diffeomorphic approximation.
Reviewer: P.Caraman

MSC:

30C62 Quasiconformal mappings in the complex plane
30E10 Approximation in the complex plane
26A16 Lipschitz (Hölder) classes
57R12 Smooth approximations in differential topology
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