Treffer: A remark on the Ahlfors-Lehto univalence criterion: A remark on the Ahlfors--Lehto univalence criterion

Title:
A remark on the Ahlfors-Lehto univalence criterion: A remark on the Ahlfors--Lehto univalence criterion
Authors:
Sugawa, Toshiyuki
Source:
Annales Fennici Mathematici; Vol. 27 No. 1 (2002): Volume 27, 2002; 151-161
Annales Fennici Mathematici; Vol 27 Nro 1 (2002): Volume 27, 2002; 151-161
Publisher Information:
The Finnish Mathematical Society, 2002.
Publication Year:
2002
Subject Terms:
General theory of univalent and multivalent functions of one complex variable, Quasiconformal mappings in the complex plane, Teichmüller theory for Riemann surfaces
Document Type:
Fachzeitschrift Article
File Description:
application/pdf; application/xml
Language:
English
Access URL:
https://afm.journal.fi/article/view/135032
https://zbmath.org/1987649
Rights:
CC BY
Accession Number:
edsair.dedup.wf.002..aad2b187d1b300143190a7c8c07797b0
Database:
OpenAIRE

Weitere Informationen

The starting point for the connection between univalence of an analytic function and the corrresponding Schwarzian derivative was a paper of \textit{W. Kraus} [Mitteil. Math. Semin. Univ. Giessen 21, 1-28 (1932; Zbl 0005.30104)] (not mentioned by the author). He derived an inequality for the Schwarzian as a necessary condition for a schlicht function in the unit disk. Later Z. Nehari found a stronger inequality which is sufficient for univalence. This condition was later generalized by L. V. Ahlfors and O. Lehto to an arbitrary quasidisk if a quasiconformal reflection is known. The author now proves this without smoothness of this reflection.