Convex equipartitions: the spicy chicken theorem

DOI10.1007/s10711-013-9879-5zbMath1301.52010arXiv1306.2741OpenAlexW1967770701MaRDI QIDQ2452181

Alfredo Hubard, Boris Aronov, Roman N. Karasev

Publication date: 30 May 2014

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.2741

zbMATH Keywords

configuration spaceVoronoi diagramBorsuk-Ulamequipartitionswaistham sandwichNandakumar-Ramana Rao conjecture

Mathematics Subject Classification ID

Length, area, volume, other geometric measure theory (28A75) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Fixed points and coincidences in algebraic topology (55M20) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (20)

Equipartitions and Mahler volumes of symmetric convex bodies ⋮ Measure partitions using hyperplanes with fixed directions ⋮ A survey of mass partitions ⋮ Tilings with noncongruent triangles ⋮ Discrete geometry on colored point sets in the plane -- a survey ⋮ Near equipartitions of colored point sets ⋮ Incongruent equipartitions of the plane ⋮ ENVY‐FREE DIVISION USING MAPPING DEGREE ⋮ Measure equipartitions via finite Fourier analysis ⋮ Thieves can make sandwiches ⋮ Convex equipartitions of colored point sets ⋮ Cutting polygons into small pieces with chords: Laser-based localization ⋮ Balanced convex partitions of lines in the plane ⋮ Vanishing of all equivariant obstructions and the mapping degree ⋮ Measure partitions via Fourier analysis. II: Center transversality in the \({{L}^{2}}\)-norm for complex hyperplanes ⋮ Convex equipartitions via equivariant obstruction theory ⋮ Tilings of the plane with unit area triangles of bounded diameter ⋮ Incongruent equipartitions of the plane into quadrangles of equal perimeters ⋮ Equilateral polygons in a Euclidean space and on deformed spheres via Fadell-Husseini index ⋮ Counterexamples to the colorful Tverberg conjecture for hyperplanes

Cites Work

• Fair partitions of polygons: an elementary introduction
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• Minkowski-type theorems and least-squares clustering
• Isoperimetry of waists and concentration of maps
• Perfect partitions of convex sets in the plane
• Existence and uniqueness of monotone measure-preserving maps
• Convex equipartitions via equivariant obstruction theory
• Partitions of a polytope and mappings of a point set to facets
• Homology theory for locally compact spaces
• Homology with local coefficients
• BALANCED CONVEX PARTITIONS OF MEASURES IN ℝ ^d
• ON GROMOV'S WAIST OF THE SPHERE THEOREM
• Polar factorization and monotone rearrangement of vector‐valued functions
• Optimal Transport
• The mod 2 equivariant cohomology algebras of configuration spaces
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