Volume difference inequalities

2016/08/11 by Giannopoulos, Apostolos, Koldobsky, Alexander
#52A20 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1608.03435

Abstract

We prove several inequalities estimating the distance between volumes of two bodies in terms of the maximal or minimal difference between areas of sections or projections of these bodies. We also provide extensions in which volume is replaced by an arbitrary measure.

Related

• Measure comparison and distance inequalities for convex bodies
• Stability and separation in volume comparison problems
• Sections of the difference body
• The boundness of distance between two sets of fixed volume inside the multidimensional ball or cube
• Estimating volume and surface area of a convex body via its projections\n or sections