On convex mappings

2018/06/20 by Chuaqui, Martin, Osgood, Brad
#30C45 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.07982

Abstract

We establish a new characterization for a conformal mapping of the unit disk \mathbbD to be convex, and identify the mappings onto a half-plane or a parallel strip as extremals. We also show that, with these exceptions, the level sets of λ of the Poincaré metric λ|dw| of a convex domain are strictly convex.

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