On convex mappings
Complex Variables
2018-08-08 v2
Abstract
We establish a new characterization for a conformal mapping of the unit disk 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 of the Poincar\'e metric of a convex domain are strictly convex.
Cite
@article{arxiv.1806.07982,
title = {On convex mappings},
author = {Martin Chuaqui and Brad Osgood},
journal= {arXiv preprint arXiv:1806.07982},
year = {2018}
}