1 results
STARLIKENESS AND CONVEXITY OF CAUCHY TRANSFORMS ON REGULAR POLYGONS
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 103 / Issue 2 / April 2021
- Published online by Cambridge University Press:
- 05 October 2020, pp. 291-302
- Print publication:
- April 2021
-
- Article
- Export citation
-
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 
$\widehat {\mathbb {C}}\setminus Q_n$
.
