$L_p$ John ellipsoids for log-concave functions
Functional Analysis
2021-07-26 v1 Metric Geometry
Abstract
The aim of this paper is to develop the John ellipsoid for the geometry of log-concave functions. Using the results of the Minkowski theory for log-concave function established in \cite{fan-xin-ye-geo2020}, we characterize the John ellipsoid for log-concave function, and establish some inequalities of the John ellipsoid for log-concave function. Finally, the analog of Ball's volume ratio inequality for the John ellipsoid of log-concave function is established.
Keywords
Cite
@article{arxiv.2107.11018,
title = {$L_p$ John ellipsoids for log-concave functions},
author = {Fangwei Chen and Jianbo Fang and Miao Luo and Congli Yang},
journal= {arXiv preprint arXiv:2107.11018},
year = {2021}
}