Commun. Math. Res., 31 (2015), pp. 161-170.
Published online: 2021-05
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Properties of the $p$-measures of asymmetry and the corresponding affine equivariant $p$-critical points, defined recently by the second author, for convex bodies are discussed in this article. In particular, the continuity of $p$-critical points with respect to $p$ on $(1, +∞)$ is confirmed, and the connections between general $p$-critical points and the Minkowski-critical points ($∞$-critical points) are investigated. The behavior of $p$-critical points of convex bodies approximating a convex bodies is studied as well.
}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2015.02.07}, url = {http://global-sci.org/intro/article_detail/cmr/18939.html} }Properties of the $p$-measures of asymmetry and the corresponding affine equivariant $p$-critical points, defined recently by the second author, for convex bodies are discussed in this article. In particular, the continuity of $p$-critical points with respect to $p$ on $(1, +∞)$ is confirmed, and the connections between general $p$-critical points and the Minkowski-critical points ($∞$-critical points) are investigated. The behavior of $p$-critical points of convex bodies approximating a convex bodies is studied as well.