On geometric estimates for univalent functions

We provide geometric estimates for conformal maps of the unit disc. As a consequence, a bound for the derivative of such maps follows yielding, in particular, an answer to a question posed by Martín Chuaqui. Finally, estimates regarding the curvature of image arcs under conformal maps are also obtai...

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Bibliographic Details
Published inAnnali di matematica pura ed applicata Vol. 200; no. 3; pp. 1075 - 1084
Main Authors Gallardo-Gutiérrez, Eva A., Pommerenke, Christian
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2021
Springer Nature B.V
Subjects
Conformal mapping
Estimates
Mathematics
Mathematics and Statistics
Original Research
Secondary 30C55
Univalent functions
Koebe distortion theorem
Geometric estimates
Primary 30C45
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Summary:We provide geometric estimates for conformal maps of the unit disc. As a consequence, a bound for the derivative of such maps follows yielding, in particular, an answer to a question posed by Martín Chuaqui. Finally, estimates regarding the curvature of image arcs under conformal maps are also obtained.
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-020-01026-w