Plane R-curves II

DOI10.1080/00036811.2019.1600677zbMath1464.49031OpenAlexW2932118129MaRDI QIDQ5148314

Paolo Manselli, Marco Longinetti, Adriana Venturi

Publication date: 3 February 2021

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036811.2019.1600677

zbMATH Keywords

rectifiabilitysets with positive reachdetoursteepest descent curveself-contracted curve

Mathematics Subject Classification ID

Geometric methods in ordinary differential equations (34A26) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Ordinary differential inclusions (34A60) Curves in Euclidean and related spaces (53A04)

Cites Work

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• Maximum length of steepest descent curves for quasi-convex functions
• Asymptotic behaviour of self-contracted planar curves and gradient orbits of convex functions
• Rectifiability of non Euclidean planar self-contracted curves
• Self-contracted curves in CAT(0)-spaces and their rectifiability
• Metric and geometric relaxations of self-contracted curves
• Rectifiability of self-contracted curves in the Euclidean space and applications
• Self-contracted curves in Riemannian manifolds
• Curvature Measures
• On steepest descent curves for quasi convex families in Rn
• Plane R-curves and their steepest descent properties I
• Self-contracted curves have finite length
• Generalized self-approaching curves

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