Analytic parametrization of three-dimensional bodies of constant width

DOI10.1007/s00205-007-0060-xzbMath1131.52002OpenAlexW2084518016MaRDI QIDQ2460230

Thomas Lachand-Robert, Térence Bayen, Edouard Oudet

Publication date: 14 November 2007

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00205-007-0060-x

zbMATH Keywords

body of constant widthmedian surface

Mathematics Subject Classification ID

Length, area, volume and convex sets (aspects of convex geometry) (52A38) Convex sets in (3) dimensions (including convex surfaces) (52A15) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (13)

Parametric shape optimization using the support function ⋮ A doubly monotone flow for constant width bodies in ℝ³ ⋮ Semidefinite programming for optimizing convex bodies under width constraints ⋮ A generalization of the Blaschke-Lebesgue problem to a kind of convex domains ⋮ Complete sets in normed linear spaces ⋮ Shape optimization under width constraint ⋮ Meissner's mysterious bodies ⋮ On the 1-measure of asymmetry for convex bodies of constant width ⋮ Asymmetry of convex bodies of constant width ⋮ Illuminating spindle convex bodies and minimizing the volume of spherical sets of constant width ⋮ On the three-dimensional Blaschke-Lebesgue problem ⋮ Minimization of the Eigenvalues of the Dirichlet-Laplacian with a Diameter Constraint ⋮ An open global volume minimization problem

Uses Software

• PETSc

Cites Work

• A direct proof of a theorem of Blaschke and Lebesgue.
• Bodies of constant width in arbitrary dimension
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