A note on the extremal noncentral sections of the cross-polytope
Metric Geometry
2020-12-08 v1
Abstract
We find minimal and maximal length of intersections of lines at a fixed distance to the origin with the cross-polytope. We also find maximal volume noncentral sections of the cross-polypote by hyperplanes which are at a fixed large distance to the origin and minimal volume sections by symmetric slabs of a large fixed width. This parallels recent results about noncentral sections of the cube due to Moody, Stone, Zach and Zvavitch.
Keywords
Cite
@article{arxiv.1910.06993,
title = {A note on the extremal noncentral sections of the cross-polytope},
author = {Ruoyuan Liu and Tomasz Tkocz},
journal= {arXiv preprint arXiv:1910.06993},
year = {2020}
}
Comments
15 pages, 2 figures