Volume of intersections and sections of the unit ball of $\ell ^n_p$

DOI10.1090/S0002-9939-98-04179-3zbMath0896.52009MaRDI QIDQ4383155

Michael Schmuckenschlaeger

Publication date: 24 March 1998

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

zbMATH Keywords

isotropic constantvolume of a Minkowski ball

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Probabilistic methods in Banach space theory (46B09) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (13)

Spectral flatness and the volume of intersections of \(p\)-ellipsoids ⋮ A note on the volume of sections of \(B_{p}^{n}\) ⋮ Estimates for the extremal sections of complex \(\ell_p\)-balls ⋮ Estimates for the extremal sections of \(\ell ^n_p\)-balls ⋮ A note about the uniform distribution on the intersection of a simplex and a sphere ⋮ Intersection of unit balls in classical matrix ensembles ⋮ Series associated to some expressions involving the volume of the unit ball and applications ⋮ Sections and projections of \(L_p\)-zonoids and their polars ⋮ Asymptotic properties of two affine invariants for 1-unconditonal convex bodies ⋮ Inequalities for the Gamma function and estimates for the volume of sections of $B^n_p$ ⋮ The Busemann-Petty problem for arbitrary measures ⋮ VOLUME ESTIMATES FOR L _p ‐ZONOTOPES AND BEST BEST CONSTANTS IN BRASCAMP–LIEB INEQUALITIES ⋮ Sylvester's problem for symmetric convex bodies and related problems

Cites Work

• Sections of the unit ball of \(\ell ^ n_ p\)
• Logarithmically concave functions and sections of convex sets in $R^{n}$
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