Estimates for the extremal sections of \(\ell ^n_p\)-balls

DOI10.1016/j.jmaa.2010.11.058zbMath1217.52005OpenAlexW2031669028MaRDI QIDQ624637

Dan Ma, Bin-Wu He

Publication date: 9 February 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2010.11.058

zbMATH Keywords

isotropic constant\(\ell ^n_p\)-spaceslicing problem

Mathematics Subject Classification ID

Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21) Asymptotic theory of convex bodies (52A23) Asymptotic theory of Banach spaces (46B06)

Related Items (2)

Estimates for the extremal sections of complex \(\ell_p\)-balls ⋮ Sections and projections of \(L_p\)-zonoids and their polars

Cites Work

• On the hyperplane conjecture for random convex sets
• Dual mixed volumes and the slicing problem
• On convex perturbations with a bounded isotropic constant
• Sections of the unit ball of \(\ell ^ n_ p\)
• A geometric inequality with applications to linear forms
• An application of the Fourier transform to sections of star bodies
• The isotropy constants of the Schatten classes are bounded
• A reduction of the slicing problem to finite volume ratio bodies.
• An isomorphic version of the slicing problem
• Gitterperiodische Punktmengen und Isoperimetrie
• Isotropic bodies and Bourgain's problem
• Inequalities for the Gamma function and estimates for the volume of sections of $B^n_p$
• Upper bounds for the volume and diameter of $m$-dimensional sections of convex bodies
• Cube Slicing in R n
• Logarithmically concave functions and sections of convex sets in $R^{n}$
• Slicing Convex Bodies-Bounds for Slice Area in Terms of the Body's Covariance
• Slicing the Cube in R n and Probability (Bounds for the Measure of a Central Cube Slice in R n by Probability Methods)
• Volume of intersections and sections of the unit ball of $\ell ^n_p$
• Extremal sections of complex l_p-balls, 0 < p ≤2
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