Estimates for moments of general measures on convex bodies

2017/12/16 by Bobkov, Sergey, Klartag, Bo'az, Koldobsky, Alexander
#52A20 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1712.05949

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 Rⁿ 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.

Related

• Measure comparison and distance inequalities for convex bodies
• Measures of sections of convex bodies
• Poincare Inequalities and Moment Maps
• Slicing inequalities for measures of convex bodies
• The Busemann-Petty problem for arbitrary measures