Volume ratios and a reverse isoperimetric inequality

1989/10/26 by Keith Ball, Ball, Keith · 5 citations
Mathematics · #52A20 #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.math/9201205

openalex publication_date 1989/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that if C is an n-dimensional convex body then there is an affine image \widetilde C of C for which |∂ \widetilde C|\over |\widetilde C|^{n-1\over n} is no larger than the corresponding expression for a regular n-dimensional ``tetrahedron''. It is also shown that among n-dimensional subspaces of L_p (for each p∈ [1,∞]), ℓⁿ_p has maximal volume ratio.\vskip3in

Cited by

• Learning Confidence Ellipsoids and Applications to Robust Subspace Recovery
• Approximate isoperimetry for convex polytopes
• Equality in Liakopoulos's generalized dual Loomis-Whitney inequality via Barthe's Reverse Brascamp-Lieb inequality
• John Ellipsoids of Revolution
• Optimal mean width and metric entropy estimates for convex bodies

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