On variational problems related to steepest descent curves and self-dual convex sets on the sphere

DOI10.1080/00036811.2014.892927zbMath1309.52005arXiv1309.0976OpenAlexW2963949473WikidataQ58159250 ScholiaQ58159250MaRDI QIDQ5175342

Adriana Venturi, Marco Longinetti, Paolo Manselli

Publication date: 20 February 2015

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

Full work available at URL: https://arxiv.org/abs/1309.0976

zbMATH Keywords

convex setsself-dual conessteepest descent curvesconstant width on the sphere

Mathematics Subject Classification ID

Length, area, volume and convex sets (aspects of convex geometry) (52A38) Convex sets in (2) dimensions (including convex curves) (52A10) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30)

Related Items (2)

Bounding regions to plane steepest descent curves of quasiconvex families ⋮ On steepest descent curves for quasi convex families in Rn

Cites Work

• Illuminating spindle convex bodies and minimizing the volume of spherical sets of constant width
• Maximum length of steepest descent curves for quasi-convex functions
• Asymptotic behaviour of self-contracted planar curves and gradient orbits of convex functions
• Self-dual cones in Euclidean spaces
• Completeness and constant width in spherical and hyperbolic spaces
• Some remarks on the class of continuous (semi-)strictly quasiconvex functions
• Curves of constant width in the non-Euclidean geometry
• Convex regions on the \(n\)-dimensional spherical surface

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