English

Extremal sections and projections of certain convex bodies: a survey

Functional Analysis 2025-01-28 v3 Metric Geometry Probability

Abstract

We survey results concerning sharp estimates on volumes of sections and projections of certain convex bodies, mainly p\ell_p balls, by and onto lower dimensional subspaces. This subject emerged from geometry of numbers several decades ago and since then has seen development of a variety of probabilistic and analytic methods, showcased in this survey.

Keywords

Cite

@article{arxiv.2210.00885,
  title  = {Extremal sections and projections of certain convex bodies: a survey},
  author = {Piotr Nayar and Tomasz Tkocz},
  journal= {arXiv preprint arXiv:2210.00885},
  year   = {2025}
}

Comments

References updated. To appear in "Harmonic Analysis and Convexity"