Slicing $\ell_p$-balls reloaded: stability, planar sections in $\ell_1$
Functional Analysis
2022-11-23 v2 Probability
Abstract
We show that the two-dimensional minimum-volume central section of the -dimensional cross-polytope is attained by the regular -gon. We establish stability-type results for hyperplane sections of -balls in all the cases where the extremisers are known. Our methods are mainly probabilistic, exploring connections between negative moments of projections of random vectors uniformly distributed on convex bodies and volume of their sections.
Keywords
Cite
@article{arxiv.2109.05645,
title = {Slicing $\ell_p$-balls reloaded: stability, planar sections in $\ell_1$},
author = {Giorgos Chasapis and Piotr Nayar and Tomasz Tkocz},
journal= {arXiv preprint arXiv:2109.05645},
year = {2022}
}
Comments
Final version. To appear in Ann. Probab