A sharp bound on the number of self-intersections of a trigonometric curve

We obtain a sharp bound on the number of self-intersections of a closed planar curve with trigonometric parameterization. Moreover, we show that a generic curve of this form is normal in the sense of Whitney.

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2025-03, Vol.543 (2), p.128995, Article 128995
Main Authors: Kalmykov, Sergei, Kovalev, Leonid V.
Format: Article
Language:English
Subjects:
Intersection multiplicity
Laurent polynomials
Self-intersections
Trigonometric curves
Whitney index
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Description
Summary:We obtain a sharp bound on the number of self-intersections of a closed planar curve with trigonometric parameterization. Moreover, we show that a generic curve of this form is normal in the sense of Whitney.
ISSN:0022-247X
DOI:10.1016/j.jmaa.2024.128995