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

Sergei Kalmykov; Leonid V. Kovalev

doi:10.1016/j.jmaa.2024.128995

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

Sergei Kalmykov, Leonid V. Kovalev

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Article number	128995
Journal	Journal of Mathematical Analysis and Applications
Volume	543
Issue number	2P1
DOIs	https://doi.org/10.1016/j.jmaa.2024.128995
State	Published - Mar 15 2025

Keywords

Intersection multiplicity
Laurent polynomials
Self-intersections
Trigonometric curves
Whitney index

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2024.128995

Cite this

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title = "A sharp bound on the number of self-intersections of a trigonometric curve",

abstract = "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.",

keywords = "Intersection multiplicity, Laurent polynomials, Self-intersections, Trigonometric curves, Whitney index",

author = "Sergei Kalmykov and Kovalev, {Leonid V.}",

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AU - Kalmykov, Sergei

AU - Kovalev, Leonid V.

PY - 2025/3/15

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N2 - 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.

AB - 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.

KW - Intersection multiplicity

KW - Laurent polynomials

KW - Self-intersections

KW - Trigonometric curves

KW - Whitney index

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JF - Journal of Mathematical Analysis and Applications

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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