Asymptotic conformality of the barycentric extension of quasiconformal maps | Zendy

Katsuhiko Matsuzaki | Zendy; Masahiro Yanagishita | Zendy

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Asymptotic conformality of the barycentric extension of quasiconformal maps

Author(s) -

Katsuhiko Matsuzaki,

Masahiro Yanagishita

Publication year - 2017

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1701085m

Subject(s) - mathematics , barycentric coordinate system , extension (predicate logic) , cusp (singularity) , conformal map , pure mathematics , homeomorphism (graph theory) , integrable system , riemann surface , embedding , mathematical analysis , quasiconformal mapping , geometry , combinatorics , artificial intelligence , computer science , programming language

We first remark that the complex dilatation of a quasiconformal homeomorphism of a hyperbolic Riemann surface $R$ obtained by the barycentric extension due to Douady-Earle vanishes at any cusp of $R$. Then we give a new proof, without using the Bers embedding, of a fact that the quasiconformal homeomorphism obtained by the barycentric extension from an integrable Beltrami coefficient on $R$ is asymptotically conformal.

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