English

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}
}