Existence et unicit 'e d'une courbe `a courbure positive maximisant le\n minimum du rayon de courbure

2021/03/29 by Jérôme Bastien, Bastien, Jérôme
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematics and Applications #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2104.01143

openalex publication_date 2021/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the set E of curves with positive algebraic curvature, whose\nextremities and tangents in their extremities are given. For each of the curves\nof E, we define the minimum of the radius of curvature. There exists a unique\ncurve of E which maximizes this minimum and this curve is equal to the unique\ncurve of E composed of an arc of circle and a line segment, where appropriate\nreduced to a point. This curve corresponds also to a particular case of\nDubins's curve and will be used to improve the conception of a piece of a\npatent.\n

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