On the three-dimensional Blaschke-Lebesgue problem

DOI10.1090/S0002-9939-2010-10588-9zbMath1226.52003arXiv0906.3217OpenAlexW2115946008MaRDI QIDQ3003594

Henri Anciaux, Brendan S. Guilfoyle

Publication date: 27 May 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.3217

zbMATH Keywords

volumeprincipal curvaturesconstant width setBlaschke-Lebesgue problem

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Convex sets in (3) dimensions (including convex surfaces) (52A15)

Related Items (12)

Parametric shape optimization using the support function ⋮ A doubly monotone flow for constant width bodies in ℝ³ ⋮ A generalization of the Blaschke-Lebesgue problem to a kind of convex domains ⋮ A new geometric structure on tangent bundles ⋮ Peabodies of constant width ⋮ Shape optimization under width constraint ⋮ Meissner polyhedra ⋮ The graphs behind reuleaux polyhedra ⋮ Meissner's mysterious bodies ⋮ Marginally trapped submanifolds in Lorentzian space forms and in the Lorentzian product of a space form by the real line ⋮ A generalization of domains of constant width ⋮ Surfaces with one constant principal curvature in three-dimensional space forms

Cites Work

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• On \(C^{2}\)-smooth surfaces of constant width
• A direct proof of a theorem of Blaschke and Lebesgue.
• Analytic parametrization of three-dimensional bodies of constant width
• Convex bodies of constant width and constant brightness
• A characterization of a standard torus in \(E^ 3\)

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