A relatively simple proof is given for Haimo’s theorem that a meromorphic function with suitably controlled Schwarzian derivative is a concave mapping. More easily verified conditions are found to imply Haimo’s criterion, which is now shown to be sharp. It is proved that Haimo’s functions map the unit disk onto the outside of an asymptotically conformal Jordan curve, thus ruling out the presence of corners.
@article{bwmeta1.element.ojs-doi-10_17951_a_2011_65_2_17-28,
author = {Martin Chuaqui and Peter Duren and Brad Osgood},
title = {On a theorem of Haimo regarding concave mappings},
journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica},
volume = {65},
year = {2011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2011_65_2_17-28}
}
Martin Chuaqui; Peter Duren; Brad Osgood. On a theorem of Haimo regarding concave mappings. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 65 (2011) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2011_65_2_17-28/
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