On the three-dimensional Blaschke-Lebesgue problem
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Publication:3003594
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
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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