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STARLIKENESS AND CONVEXITY OF CAUCHY TRANSFORMS ON REGULAR POLYGONS
Published online by Cambridge University Press: 05 October 2020
Abstract
For $n\geq 3$ , let $Q_n\subset \mathbb {C}$ be an arbitrary regular n-sided polygon. We prove that the Cauchy transform $F_{Q_n}$ of the normalised two-dimensional Lebesgue measure on $Q_n$ is univalent and starlike but not convex in $\widehat {\mathbb {C}}\setminus Q_n$ .
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- © 2020 Australian Mathematical Publishing Association Inc.
Footnotes
This research is supported in part by the NNSF of China (No. 11831007).