A note on convex conformal mappings

Chuaqui, Martin; Osgood, Brad

doi:10.1090/proc/14429

A note on convex conformal mappings
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by Martin Chuaqui and Brad Osgood PDF

Proc. Amer. Math. Soc. 147 (2019), 2655-2659 Request permission

Abstract:

We establish a new characterization for a conformal mapping of the unit disk $\mathbb {D}$ 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 $\lambda$ of the Poincaré metric $\lambda |dw|$ of a convex domain are strictly convex.

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