On the equivalence between two problems of asymmetry on convex bodies
Functional Analysis
2014-11-25 v2
Abstract
The simplex was conjectured to be the extremal convex body for the two following "problems of asymmetry":\\ P1) What is the minimal possible value of the quantity ? Here, ranges over all symmetric convex bodies contained in .\\ P2) What is the maximal possible volume of the Blaschke-body of a convex body of volume 1?\\ Our main result states that (P1) and (P2) admit precisely the same solutions. This complements a result from [{\rm K. B\"or\"oczky, I. B\'ar\'any, E. Makai Jr. and J. Pach}, Maximal volume enclosed by plates and proof of the chessboard conjecture], Discrete Math. {\bf 69} (1986), 101--120], stating that if the simplex solves (P1) then the simplex solves (P2) as well.
Cite
@article{arxiv.1311.4955,
title = {On the equivalence between two problems of asymmetry on convex bodies},
author = {Christos Saroglou},
journal= {arXiv preprint arXiv:1311.4955},
year = {2014}
}
Comments
A serious logical gap fixed, from the previous version