Concave functions, blaschke products, and polygonal mappings
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- Bhowmik, B., Ponnusamy, S. & Wirths, K.J. Sib Math J (2009) 50: 609. doi:10.1007/s11202-009-0068-6
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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).