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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
$\widehat {\mathbb {C}}\setminus Q_n$
.
- Type
- Research Article
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- Copyright
- © 2020 Australian Mathematical Publishing Association Inc.
Footnotes
This research is supported in part by the NNSF of China (No. 11831007).