Quasisymmetric boundary correspondence and Grötzsch problem

Two necessary and sufficient conditions for the validity of the conjectureK0(h) =K1(h) are given, which are independent of the complex dilatations of extremal quasiconformal mappings, where K0(h) is the maximal conformal modulus dilatation of the boundary homeomorphismh, K1(h) is the maximal dilatat...

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Bibliographic Details
Published inChinese science bulletin Vol. 43; no. 12; pp. 992 - 994
Main Authors Zemin, Wu, Wancai, Lai
Format Journal Article
LanguageEnglish
Published Beijing Springer Nature B.V 01.06.1998
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Summary:Two necessary and sufficient conditions for the validity of the conjectureK0(h) =K1(h) are given, which are independent of the complex dilatations of extremal quasiconformal mappings, where K0(h) is the maximal conformal modulus dilatation of the boundary homeomorphismh, K1(h) is the maximal dilatation of extremal quasiconformal mappings that agree withh on the boundary. In addition, when the complex dilatation of an extremal quasiconformal mapping is known, the proof of the result simplifies Reich and Chen Jixiu-Chen Zhiguo’s result.
ISSN:1001-6538
2095-9273
1861-9541
2095-9281
DOI:10.1007/BF02884631