On Properties of $p$-Critical Points of Convex Bodies (Communications in Mathematical Research, 2021)
Properties of the $p$-measures of asymmetry and the corresponding affineequivariant $p$-critical points, defined recently by the second author, for convex bodiesare discussed in this article. In particular, the continuity of $p$-critical points withrespect to $p$ on $(1, +∞)$ is confirmed, and the connections between general $p$-criticalpoints and the Minkowski-critical points ($∞$-critical points) are investigated. Thebehavior of $p$-critical points of convex bodies approximating a convex bodies is studiedas well.