Sections of convex bodies in John's and minimal surface area position
Metric Geometry
2020-12-21 v1 Functional Analysis
Abstract
We prove several estimates for the volume, mean width, and the value of the Wills functional of sections of convex bodies in John's position, as well as for their polar bodies. These estimates extend some well-known results for convex bodies in John's position to the case of lower-dimensional sections, which had mainly been studied for the cube and the regular simplex. Some estimates for centrally symmetric convex bodies in minimal surface area position are also obtained.
Keywords
Cite
@article{arxiv.2012.10166,
title = {Sections of convex bodies in John's and minimal surface area position},
author = {David Alonso-Gutiérrez and Silouanos Brazitikos},
journal= {arXiv preprint arXiv:2012.10166},
year = {2020}
}