A very short proof of the Figiel-Lindenstrauss-Milman theorem

We provide a short proof for the Figiel, Lindenstrauss and Milman inequality regarding the number of vertices and faces of certain polytope, with an explicit bound on the universal constant involved. The proof is completely elementary and avoids any form of Dvoretzky's theorem, as well as the spherical isoperimetric inequality.

Publication Details

Journal
ArXiv.org
Published
2025-03-17
Primary Topic
Point processes and geometric inequalities
Type
article
Field-Weighted Citation Impact
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article

A very short proof of the Figiel-Lindenstrauss-Milman theorem

ArXiv.org
Point processes and geometric inequalities
article

A very short proof of the Figiel-Lindenstrauss-Milman theorem

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Abstract

We provide a short proof for the Figiel, Lindenstrauss and Milman inequality regarding the number of vertices and faces of certain polytope, with an explicit bound on the universal constant involved. The proof is completely elementary and avoids any form of Dvoretzky's theorem, as well as the spherical isoperimetric inequality.

ArXiv.org
Reduced inequalities
Openalex Percentile: Top 39%
Point processes and geometric inequalities
Open Access PDFOpenAlex
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A very short proof of the Figiel-Lindenstrauss-Milman theorem · ArXiv.org (2025) | TGRS Research Map | TGRS