Self-contracted curves in Riemannian manifolds

DOI10.1016/j.jmaa.2017.04.011zbMath1376.53073OpenAlexW2602919751WikidataQ115345995 ScholiaQ115345995MaRDI QIDQ2408638

Estibalitz Durand-Cartagena, Ludovic Rifford, Robert Deville, Aris Daniilidis

Publication date: 12 October 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2017.04.011

zbMATH Keywords

Riemannian manifoldlengthrectifiable curvesecantself-contracted curveself-expanded curve

Mathematics Subject Classification ID

Global submanifolds (53C40)

Related Items (12)

Riemannian proximal gradient methods ⋮ A connection between cut locus, Thom space and Morse-Bott functions ⋮ A semismooth Newton based augmented Lagrangian method for nonsmooth optimization on matrix manifolds ⋮ Unnamed Item ⋮ Ubiquitous algorithms in convex optimization generate self-contracted sequences ⋮ Self-contracted curves are gradient flows of convex functions ⋮ Plane R-curves II ⋮ Rectifiability of non Euclidean planar self-contracted curves ⋮ SRA-free condition by Zolotov for self-contracted curves and nondegeneracy of the zz-distance for Möbius structures on the circle ⋮ Self-contracted curves in CAT(0)-spaces and their rectifiability ⋮ Metric and geometric relaxations of self-contracted curves ⋮ Straightening warped cones

Cites Work

• Maximum length of steepest descent curves for quasi-convex functions
• Asymptotic behaviour of self-contracted planar curves and gradient orbits of convex functions
• Steepest descent curves of convex functions on surfaces of constant curvature
• Rectifiability of non Euclidean planar self-contracted curves
• Rectifiability of self-contracted curves in the Euclidean space and applications
• Orbits of Geometric Descent
• On steepest descent curves for quasi convex families in Rn
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