Asymptotic estimates for the largest volume ratio of a convex body

DOI10.4171/rmi/1263zbMath1472.52008arXiv1901.00771OpenAlexW3138461027MaRDI QIDQ1982553

Damián Pinasco, Mariano Merzbacher, Daniel Galicer

Publication date: 14 September 2021

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.00771

zbMATH Keywords

volume ratioSchatten classesunconditional convex bodiesrandom polytopes

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21) Asymptotic theory of convex bodies (52A23)

Related Items

On the volume ratio of projections of convex bodies

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On determinants and the volume of random polytopes in isotropic convex bodies
• Exact asymptotic volume and volume ratio of Schatten unit balls
• On convex perturbations with a bounded isotropic constant
• Concentration of mass on the Schatten classes
• Volume estimates in spaces of homogeneous polynomials
• Diameter of the Minkowski compactum is approximately equal to n
• Approximation of convex bodies by centrally symmetric bodies
• The isotropy constants of the Schatten classes are bounded
• The minimal volume of simplices containing a convex body
• Generalized volume ratios and the Banach-Mazur distance.
• Distances between non-symmetric convex bodies and the \(MM^*\)-estimate
• On the thin-shell conjecture for the Schatten classes
• John's decomposition in the general case and applications
• On some Banach lattices
• Volume Ratios and a Reverse Isoperimetric Inequality
• Approximation of the Sphere by Polytopes having Few Vertices
• ON THE VOLUME RATIO OF TWO CONVEX BODIES
• High-Dimensional Probability
• Invariances in variance estimates
• Asymptotic Geometric Analysis, Part I
• Convex and Discrete Geometry
• Alice and Bob Meet Banach
• On parallelepipeds of minimal volume containing a convex symmetric body in ℝⁿ
• Absolute and Unconditional Convergence in Normed Linear Spaces
• John's theorem for an arbitrary pair of convex bodies