BRASCAMP–LIEB INEQUALITY AND QUANTITATIVE VERSIONS OF HELLY'S THEOREM

DOI10.1112/S0025579316000255zbMath1364.26025arXiv1509.05783OpenAlexW2963928068MaRDI QIDQ2970179

Silouanos Brazitikos

Publication date: 28 March 2017

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.05783

zbMATH Keywords

Helly's theoremBrascamp-Lieb inequalityJohn decompositions

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Helly-type theorems and geometric transversal theory (52A35) Asymptotic theory of convex bodies (52A23) Asymptotic theory of Banach spaces (46B06)

Related Items

Continuous version of the approximate geometric Brascamp-Lieb inequalities ⋮ Isometric and affine copies of a set in volumetric Helly results ⋮ A Quantitative Helly-Type Theorem: Containment in a Homothet ⋮ Unnamed Item ⋮ Quantitative Helly-type theorems via sparse approximation ⋮ Inequality on the optimal constant of Young's convolution inequality for locally compact groups and their closed subgroups ⋮ Helly’s theorem: New variations and applications ⋮ Colorful Helly-type theorems for the volume of intersections of convex bodies ⋮ The minimal volume of simplices containing a convex body ⋮ Quantitative fractional Helly and \((p,q)\)-theorems ⋮ Quantitative Helly-type theorem for the diameter of convex sets ⋮ Quantitative combinatorial geometry for concave functions ⋮ A Mélange of Diameter Helly-Type Theorems ⋮ Continuous quantitative Helly-type results ⋮ Functional John ellipsoids

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Gelfand numbers of operators with values in a Hilbert space
• Best constants in Young's inequality, its converse, and its generalization to more than three functions
• Umbrellas and polytopal approximation of the Euclidean ball
• Contact points of convex bodies
• New volume ratio properties for convex symmetric bodies in \({\mathbb{R}}^ n\)
• Constructing a polytope to approximate a convex body
• Interlacing families. II: Mixed characteristic polynomials and the Kadison-Singer problem
• Quantitative Tverberg theorems over lattices and other discrete sets
• Approximation of convex sets by polytopes
• Helly’s theorem: New variations and applications
• Thrifty Approximations of Convex Bodies by Polytopes
• Helly's Theorem with Volumes
• Volume Ratios and a Reverse Isoperimetric Inequality
• Convex Bodies with Few Faces
• Quantitative Helly-Type Theorems
• A Remark on Vertex Index of the Convex Bodies
• On Contact Points of Convex Bodies
• Twice-ramanujan sparsifiers
• Approximating Matrices and Convex Bodies
• Asymptotic Geometric Analysis, Part I
• Convex Bodies The Brunn-MinkowskiTheory
• On parallelepipeds of minimal volume containing a convex symmetric body in ℝⁿ
• Absolute and Unconditional Convergence in Normed Linear Spaces
• Proof of a conjecture of Bárány, Katchalski and Pach