The Alon--Milman Theorem for non-symmetric bodies

Marton Naszodi

The Alon--Milman Theorem for non-symmetric bodies

Metric Geometry 2018-05-08 v1

Authors: Marton Naszodi

Abstract

A classical theorem of Alon and Milman states that any $d$ dimensional centrally symmetric convex body has a projection of dimension $m\geq e^{c\sqrt{\ln{d}}}$ which is either close to the $m$ -dimensional Euclidean ball or to the $m$ -dimensional cross-polytope. We extended this result to non-symmetric convex bodies.

Keywords

alon-milman theorem non-symmetric convex bodies central projection euclidean ball cross-polytope

Cite

@article{arxiv.1805.02531,
  title  = {The Alon--Milman Theorem for non-symmetric bodies},
  author = {Marton Naszodi},
  journal= {arXiv preprint arXiv:1805.02531},
  year   = {2018}
}

Comments

4 pages

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