Stochastic reverse isoperimetric inequalities in the plane
Functional Analysis
2021-09-27 v1 Metric Geometry
Probability
Abstract
In recent years, it has been shown that some classical inequalities follow from a local stochastic dominance for naturally associated random polytopes. We strengthen planar isoperimetric inequalities by attaching a stochastic model to some classical inequalities, such as Mahler's Theorem, and a reverse Lutwak-Zhang inequality, the polar for centroid bodies. In particular, we obtain the dual counterpart to a result of Bisztriczky-B\"or\"oczky.
Keywords
Cite
@article{arxiv.2109.01086,
title = {Stochastic reverse isoperimetric inequalities in the plane},
author = {Jesus Rebollo Bueno},
journal= {arXiv preprint arXiv:2109.01086},
year = {2021}
}