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 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"