Slicing inequalities for subspaces of $L_p$

DOI10.1090/proc12708zbMath1339.52008arXiv1310.8102OpenAlexW2963420201MaRDI QIDQ2789876

Alexander L. Koldobsky

Publication date: 2 March 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.8102

zbMATH Keywords

intersection bodiesstability inequalitiesslicing inequalitieshyperplane problem of Bourgain

Mathematics Subject Classification ID

Local theory of Banach spaces (46B07) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items

A Remark on Measures of Sections of $$\boldsymbol{L}_{p}$$ -balls, Inequalities for the derivatives of the Radon transform on convex bodies, A discrete version of Koldobsky's slicing inequality, On the average volume of sections of convex bodies, Volume difference inequalities, An isomorphic version of the Busemann-Petty problem for arbitrary measures, A general slicing inequality for measures of convex bodies

Cites Work

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• A hyperplane inequality for measures of convex bodies in \(\mathbb R^{n }, \; n\leq 4\)
• Positive definite distributions and normed spaces
• Stability in the Busemann-Petty and Shephard problems
• Dual mixed volumes and the slicing problem
• Generalized intersection bodies
• On convex perturbations with a bounded isotropic constant
• Intersection bodies and dual mixed volumes
• A generalization of the Busemann-Petty problem on sections of convex bodies
• A \(\sqrt{n}\) estimate for measures of hyperplane sections of convex bodies
• Generalized intersection bodies are not equivalent
• Intersection bodies and \(L_{p}\)-spaces
• Counterexamples to convexity of $k$-intersection bodies
• On strict inclusions in hierarchies of convex bodies
• On High Dimensional Maximal Functions Associated to Convex Bodies
• Convolutions, Transforms, and Convex Bodies
• Finite dimensional subspaces of $L_{p}$
• Positive Definite Distributions and Subspaces of L__p With Applications to Stable Processes
• Hyperplane conjecture for quotient spaces of L p
• Sections of Convex Bodies
• Stability and Separation in Volume Comparison Problems
• The Geometry of L₀
• Inequalities of the Kahane–Khinchin type and sections of L_p-balls
• A functional analytic approach to intersection bodies