Upper bounds for the volume and diameter of $m$-dimensional sections of convex bodies
DOI10.1090/S0002-9939-07-08693-5zbMath1132.52004MaRDI QIDQ3430194
Publication date: 21 March 2007
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
isotropic constantisotropic positionslicing problemcentral sectionscircumradius of a bodydiameter of sections
Geometry and structure of normed linear spaces (46B20) Local theory of Banach spaces (46B07) 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) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)
Related Items (2)
Cites Work
- Asymptotic formulas for the diameter of sections of symmetric convex bodies
- Concentration of mass on isotropic convex bodies
- On convex perturbations with a bounded isotropic constant
- Asymptotic theory of finite dimensional normed spaces. With an appendix by M. Gromov: Isoperimetric inequalities in Riemannian manifolds
- Extremal problems and isotropic positions of convex bodies
- New volume ratio properties for convex symmetric bodies in \({\mathbb{R}}^ n\)
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- How small can the intersection of a few rotations of a symmetric convex body be?
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- A geometric inequality and a low 𝑀-estimate
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