Siberian Mathematical Journal

, Volume 50, Issue 4, pp 609–615

Concave functions, blaschke products, and polygonal mappings

Article

DOI: 10.1007/s11202-009-0068-6

Cite this article as:
Bhowmik, B., Ponnusamy, S. & Wirths, K.J. Sib Math J (2009) 50: 609. doi:10.1007/s11202-009-0068-6

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).

Keywords

concave function convex hull extreme point 

Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Indian Institute of Technology MadrasChennaiIndia
  2. 2.Institute for AnalysisTU BraunschweigBraunschweigGermany

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