On a theorem of Haimo regarding concave mappings
Martin Chuaqui; Peter Duren; Brad Osgood
Annales UMCS, Mathematica (2011)
- Volume: 65, Issue: 2, page 17-28
- ISSN: 2083-7402
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topMartin Chuaqui, Peter Duren, and Brad Osgood. "On a theorem of Haimo regarding concave mappings." Annales UMCS, Mathematica 65.2 (2011): 17-28. <http://eudml.org/doc/268263>.
@article{MartinChuaqui2011,
abstract = {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.},
author = {Martin Chuaqui, Peter Duren, Brad Osgood},
journal = {Annales UMCS, Mathematica},
keywords = {Concave mapping; Schwarzian derivative; Schwarzian norm; Haimo's theorem; univalence; Sturm comparison; asymptotically conformal curve; concave mapping},
language = {eng},
number = {2},
pages = {17-28},
title = {On a theorem of Haimo regarding concave mappings},
url = {http://eudml.org/doc/268263},
volume = {65},
year = {2011},
}
TY - JOUR
AU - Martin Chuaqui
AU - Peter Duren
AU - Brad Osgood
TI - On a theorem of Haimo regarding concave mappings
JO - Annales UMCS, Mathematica
PY - 2011
VL - 65
IS - 2
SP - 17
EP - 28
AB - 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.
LA - eng
KW - Concave mapping; Schwarzian derivative; Schwarzian norm; Haimo's theorem; univalence; Sturm comparison; asymptotically conformal curve; concave mapping
UR - http://eudml.org/doc/268263
ER -
References
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