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REGULARITY OF CURVES WITH A CONTINUOUS TANGENT LINE

Published online by Cambridge University Press:  01 February 2009

J. M. BURGUÉS*
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain (email: [email protected])
J. CUFÍ
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain (email: [email protected])
*
For correspondence; e-mail: [email protected]
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Abstract

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This note contains a proof of the fact that a Jordan curve in ℝ2 with a continuous tangent line at each point admits a regular reparameterization. We extend the result both to more general curves in ℝn and to higher orders of differentiability.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

The authors have been partially supported by MEC grant no. MTM2005-08984-CO and by grant no. 2005SGR00611 of Generalitat de Catalunya.

References

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[3]Pommerenke, Ch., Boundary Behaviour of Conformal Maps, Grundlehren der Mathematischen Wissenschaften, 299 (Springer, Berlin, 1992).CrossRefGoogle Scholar