From intersection bodies to dual centroid bodies: a stochastic approach to isoperimetry
Metric Geometry
2022-11-30 v1 Functional Analysis
Probability
Abstract
We establish a family of isoperimetric inequalities for sets that interpolate between intersection bodies and dual Lp centroid bodies. This provides a bridge between the Busemann intersection inequality and the Lutwak--Zhang inequality. The approach depends on new empirical versions of these inequalities.
Keywords
Cite
@article{arxiv.2211.16263,
title = {From intersection bodies to dual centroid bodies: a stochastic approach to isoperimetry},
author = {Radoslaw Adamczak and Grigoris Paouris and Peter Pivovarov and Paul Simanjuntak},
journal= {arXiv preprint arXiv:2211.16263},
year = {2022}
}