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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Simple curves in $\mathbb{R} ^n$ 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
Published electronically: June 12, 2003
MathSciNet review: 2021266
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Abstract: We derive sharp injectivity criteria for mappings $f:(-1,1)\rightarrow\mathbb{R} ^n$ in terms of Ahlfors' definition of the Schwarzian derivative for such mappings.


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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
Published electronically: 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