Estimates for moments of general measures on convex bodies
Metric Geometry
2017-12-19 v1
Abstract
We prove several estimates for the moments of arbitrary measures on convex bodies. We apply these estimates to show a new slicing inequality for measures on convex bodies. We also deduce estimates for the outer volume ratio distance from an arbitrary centrally-symmetric convex body in R^n to the class of unit balls of n-dimensional subspaces of L_p-spaces. Finally, we prove a result of the Busemann-Petty type for these moments.
Keywords
Cite
@article{arxiv.1712.05949,
title = {Estimates for moments of general measures on convex bodies},
author = {Sergey Bobkov and Bo'az Klartag and Alexander Koldobsky},
journal= {arXiv preprint arXiv:1712.05949},
year = {2017}
}