, Volume 50, Issue 4, pp 609-615
Date: 11 Aug 2009

Concave functions, blaschke products, and polygonal mappings

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Abstract

We consider the class Co(p) of all conformal maps of the unit disk onto the exterior of a bounded convex set. We prove that the triangle mappings, i.e., the functions that map the unit disk onto the exterior of a triangle, are among the extreme points of the closed convex hull of Co(p). Moreover, we prove a conjecture on the closed convex hull of Co(p) for all p ∈ (0, 1) which had partially been proved by the authors for some values of p ∈ (0, 1).

Original Russian Text Copyright © 2009 Bhowmik B., Ponnusamy S., and Wirths K.-J.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 4, pp. 772–779, July–August, 2009.