A construction of trivial beltrami coefficients

研究成果: Article査読

1 被引用数 (Scopus)

抄録

A measurable function μ on the unit disk D of the complex plane with ‖μ‖ < 1 is sometimes called a Beltrami coefficient. We say that μ is trivial if it is the complex dilatation (Formula Presented) of a quasiconformal automorphism f of D satisfying the trivial boundary condition f (z) = z, |z| = 1. Since it is not easy to solve the Beltrami equation explicitly, to detect triviality of a given Beltrami coefficient is a hard problem, in general. In the present article, we offer a sufficient condition for a Beltrami coefficient to be trivial. Our proof is based on Betker’s theorem on Löwner chains.

本文言語English
ページ(範囲)629-635
ページ数7
ジャーナルProceedings of the American Mathematical Society
147
2
DOI
出版ステータスPublished - 2019 2

ASJC Scopus subject areas

  • 数学 (全般)
  • 応用数学

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