# 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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