Let ΓR be the class of plane, oriented, rectifiable curves γ, such that, for almost every x∈γ, the part of γ preceding x is outside the open disk of radius R, centered in x+Rtx, where tx is the unit tangent vector at x. In Longinetti et al. [Plane R-curves and their steepest descent properties I Appl Anal. DOI: 10.1080/00036811.2018.1466278], the present authors have obtained bounds for the length and the detour for C1 regular curves in ΓR. These bounds are proved here for all curves in ΓR.
Plane R-curves II / Longinetti, M.*; Manselli, P.; Venturi, A.. - In: APPLICABLE ANALYSIS. - ISSN 0003-6811. - ELETTRONICO. - (2021), pp. 1-15. [10.1080/00036811.2019.1600677]
Plane R-curves II
Longinetti, M.
;Manselli, P.;Venturi, A.
2021
Abstract
Let ΓR be the class of plane, oriented, rectifiable curves γ, such that, for almost every x∈γ, the part of γ preceding x is outside the open disk of radius R, centered in x+Rtx, where tx is the unit tangent vector at x. In Longinetti et al. [Plane R-curves and their steepest descent properties I Appl Anal. DOI: 10.1080/00036811.2018.1466278], the present authors have obtained bounds for the length and the detour for C1 regular curves in ΓR. These bounds are proved here for all curves in ΓR.
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Plane R curves II.pdf
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gapaRsdc-II-2019-02-22.pdf
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