Electrostatic capacity and measure of asymmetry

Abstract

In this paper, the p p -Minkowski capacity measures of asymmetry in terms of the q q -mixed capacity, which have the well-known Minkowski measure of asymmetry as a special case, are defined, and some properties of these measures are studied. In addition, we extend the p p -Minkowski capacity measures of asymmetry to the corresponding Orlicz version.

The Minkowski Measure of Asymmetry for Spherical Bodies of Constant Width

“…For the new development of the research of the Minkowski measure of asymmetry, see Refs. [2][3][4][5][6][7].…”

“…A special measure of asymmetry for convex bodies of constant width in R 2 was introduced by Groemer and Wallen [9] . The Minkowski measure of asymmetry for convex bodies of constant width was studied by Guo and Jin [3,5,6,10,11] . In the sense of Minkowski measure of asymmetry, the complete bodies of the regular simplex are the most asymmetric convex bodies of constant width, and the Euclidean balls are the most symmetric convex bodies of constant width.…”