Measures of Asymmetry Dual to Mean Minkowski Measures of Asymmetry for Convex Bodies (Communications in Mathematical Research, 2021)
We introduce a family of measures (functions) of asymmetry for convexbodies and discuss their properties. It turns out that this family of measures sharesmany nice properties with the mean Minkowski measures. As the mean Minkowskimeasures describe the symmetry of lower dimensional sections of a convex body, thesenew measures describe the symmetry of lower dimensional orthogonal projections.
Keywords: mean Minkowski measure; asymmetry; symmetry; simplex.