A note on a theorem of Chuaqui and Gevirtz

Yong Chan Kim, Toshiyuki Sugawa

Research output: Contribution to journalArticle

Abstract

For a subdomain Ω of the right half-plane H; Chuaqui and Gevirtz showed the following theorem: the image f(D) of the unit disk D under an analytic function f on D is a quasidisk whenever f″(D) ⊂ Ω if and only if there exists a compact subset K of H such that sK ∩ (H \ Ω) ≠ φ for any positive number s: We show that this condition is equivalent to the inequality W(Ω) < 2; where W(Ω) stands for the circular width of the domain Ω.

Original languageEnglish
Pages (from-to)273-279
Number of pages7
JournalAnnales Academiae Scientiarum Fennicae Mathematica
Volume33
Publication statusPublished - 2008 Dec 1
Externally publishedYes

Keywords

  • Noshiro-Warschawski theorem
  • Pre-Schwarzian derivative
  • Quasidisk

ASJC Scopus subject areas

  • Mathematics(all)

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