Colorful Helly-type theorems for the volume of intersections of convex bodies

DOI10.1016/j.jcta.2020.105361zbMath1456.52008arXiv1909.04997OpenAlexW3105314861MaRDI QIDQ2221836

Márton Naszódi, Viktória Földvári, Gábor Damásdi

Publication date: 2 February 2021

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.04997

zbMATH Keywords

ellipsoidintersection of convex setscolorful Helly theoremvolume of intersectionvolume of convex bodies

Mathematics Subject Classification ID

Length, area, volume and convex sets (aspects of convex geometry) (52A38) Helly-type theorems and geometric transversal theory (52A35)

Related Items (6)

Isometric and affine copies of a set in volumetric Helly results ⋮ Quantitative fractional Helly and \((p,q)\)-theorems ⋮ Quantitative combinatorial geometry for concave functions ⋮ A Mélange of Diameter Helly-Type Theorems ⋮ Continuous quantitative Helly-type results ⋮ Helly-type problems

Cites Work

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• Minimal ellipsoids and their duals
• A generalization of Caratheodory's theorem
• Helly numbers of algebraic subsets of \(\mathbb{R}^{d}\) and an extension of Doignon's theorem
• Über einige Affinvarianten konvexer Bereiche
• BRASCAMP–LIEB INEQUALITY AND QUANTITATIVE VERSIONS OF HELLY'S THEOREM
• Quantitative Helly-Type Theorems
• The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg
• Proof of a conjecture of Bárány, Katchalski and Pach

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