Volume 31, Issue 2
On Properties of $p$-Critical Points of Convex Bodies

Commun. Math. Res., 31 (2015), pp. 161-170.

Published online: 2021-05

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• Abstract

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.

• Keywords

convex body, $p$-Critical point, Minkowski measure of asymmetry, $p$-measure of asymmetry

52A38

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@Article{CMR-31-161, author = {Xing and Huang and and 19322 and and Xing Huang and Qi and Guo and and 19323 and and Qi Guo}, title = {On Properties of $p$-Critical Points of Convex Bodies}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {31}, number = {2}, pages = {161--170}, abstract = {

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} }
TY - JOUR T1 - On Properties of $p$-Critical Points of Convex Bodies AU - Huang , Xing AU - Guo , Qi JO - Communications in Mathematical Research VL - 2 SP - 161 EP - 170 PY - 2021 DA - 2021/05 SN - 31 DO - http://doi.org/10.13447/j.1674-5647.2015.02.07 UR - https://global-sci.org/intro/article_detail/cmr/18939.html KW - convex body, $p$-Critical point, Minkowski measure of asymmetry, $p$-measure of asymmetry AB -

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.

Xing Huang & Qi Guo. (2021). On Properties of $p$-Critical Points of Convex Bodies. Communications in Mathematical Research . 31 (2). 161-170. doi:10.13447/j.1674-5647.2015.02.07
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