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Simple curves in  and Ahlfors' Schwarzian derivative
Authors:
Martin Chuaqui and Julian Gevirtz
Journal:
Proc. Amer. Math. Soc. 132 (2004), 223-230
MSC (2000):
Primary 53A04, 53A55; Secondary 30C55
Posted:
June 12, 2003
MathSciNet review:
2021266
Full-text PDF Free Access
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Additional Information
Abstract: We derive sharp injectivity criteria for mappings  in terms of Ahlfors' definition of the Schwarzian derivative for such mappings.
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V. Ahlfors, Cross-ratios and Schwarzian derivatives in
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pp. 1–15. MR 981397
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Zeev
Nehari, The Schwarzian derivative and schlicht
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(10,696e), http://dx.doi.org/10.1090/S0002-9904-1949-09241-8
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537795 (80i:30033)
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 , Complex Analysis, 1-15, Birkhäuser, Basel, 1988. MR 90a:30055
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- Z. Nehari, The Schwarzian derivative and schlicht functions, Bull. Amer. Math. Soc. 55 (1949), 545-551. MR 10:696e
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- Z. Nehari, Univalence criteria depending on the Schwarzian derivative, Illinois J. Math. 23 (1979), 345-351. MR 80i:30033
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Additional Information
Martin Chuaqui
Affiliation:
Facultad de Matemáticas, P. Universidad Católica de Chile, Casilla 306, Santiago 22, Chile
Email:
mchuaqui@mat.puc.cl
Julian Gevirtz
Affiliation:
Facultad de Matemáticas, P. Universidad Católica de Chile, Casilla 306, Santiago 22, Chile
Email:
jgevirtz@mat.puc.cl
DOI:
http://dx.doi.org/10.1090/S0002-9939-03-07013-8
PII:
S 0002-9939(03)07013-8
Keywords:
Schwarzian derivative,
Nehari criteria,
injectivity,
extremal function
Received by editor(s):
January 3, 2002
Received by editor(s) in revised form:
September 5, 2002
Posted:
June 12, 2003
Additional Notes:
Both authors were partially supported by Fondecyt Grants # 1000627 and # 7000627
Communicated by:
Juha M. Heinonen
Article copyright:
© Copyright 2003 American Mathematical Society
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