Bhowmik, B.; Ponnusamy, S.; Wirths, K.-J. Unbounded convex polygons, Blaschke products and concave schlicht functions. (English) Zbl 1161.30006 Indian J. Math. 50, No. 2, 339-349 (2008). Summary: We consider conformal maps \(f\) of the open unit disc \(\mathbb D\) onto a concave domain, i.e., a domain whose complement with respect to \(\mathbb C\) is convex and unbounded. We say that \(f\) is a concave schlicht function if \(f(\mathbb D)\) is a concave domain. We also fix an opening angle for the domain \(f(\mathbb D)\) at \(\infty\) which is less than or equal to \(\pi A\), \(A\in \{1,2\}\), and denote this class of functions by \(CO(A)\). In this paper we prove a representation formula using Blaschke products for those members \(f\) of \(CO(A)\) for which the exterior of \(f(\mathbb D)\) is a convex unbounded polygon. Further, we present some examples supporting our conjecture that these polygonal maps are extreme points of the class \(CO(A)\). Cited in 1 ReviewCited in 3 Documents MSC: 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) Keywords:concave schlicht functions; extreme points PDFBibTeX XMLCite \textit{B. Bhowmik} et al., Indian J. Math. 50, No. 2, 339--349 (2008; Zbl 1161.30006)