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

 

Integral conditions on the Schwarzian for curves to be simple or unknotted


Author: Martin Chuaqui
Journal: Proc. Amer. Math. Soc. 138 (2010), 1811-1819
MSC (2000): Primary 53A04, 53A55; Secondary 34C10
Published electronically: January 6, 2010
MathSciNet review: 2587466
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Abstract: By considering integral bounds on the Schwarzian derivative we extend previous results on sufficient conditions for curves in euclidean spaces to be simple or unknotted. The conditions are optimal.


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Additional Information

Martin Chuaqui
Affiliation: Facultad de Matemáticas, Pontificia Universidad Católica de Chile (PUC), Avenida Vicuña Mackenna 4860, Santiago, Chile
Email: mchuaqui@mat.puc.cl

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10249-4
PII: S 0002-9939(10)10249-4
Keywords: Ahlfors' Schwarzian, simple curves, knots, M\"{o}bius transformation
Received by editor(s): November 24, 2008
Published electronically: January 6, 2010
Additional Notes: This work was partially supported by Fondecyt Grant 1071019.
Communicated by: Mario Bank
Article copyright: © Copyright 2010 American Mathematical Society