Uniqueness and Continuity of the Solution to $$L_p$$ Dual Minkowski Problem

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-08 DOI:10.1007/s40304-023-00374-2

Hejun Wang, Jiazu Zhou

引用次数: 0

Abstract

Lutwak et al. (Adv Math 329:85–132, 2018) introduced the $L_p$ dual curvature measure that unifies several other geometric measures in dual Brunn–Minkowski theory and Brunn–Minkowski theory. Motivated by works in Lutwak et al. (Adv Math 329:85–132, 2018), we consider the uniqueness and continuity of the solution to the $L_p$ dual Minkowski problem. To extend the important work (Theorem A) of LYZ to the case for general convex bodies, we establish some new Minkowski-type inequalities which are closely related to the optimization problem associated with the $L_p$ dual Minkowski problem. When $q< p$, the uniqueness of the solution to the $L_p$ dual Minkowski problem for general convex bodies is obtained. Moreover, we obtain the continuity of the solution to the $L_p$ dual Minkowski problem for convex bodies.

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$$L_p$$ 双闵科夫斯基问题解的唯一性和连续性

Lutwak 等人（Adv Math 329:85-132, 2018）引入了 $L_p$ 对偶曲率度量，该度量统一了对偶布鲁恩-闵科夫斯基理论和布鲁恩-闵科夫斯基理论中的其他几个几何度量。受卢特瓦克等人的研究（Adv Math 329:85-132，2018）的启发，我们考虑了 $L_p$ 对偶闵科夫斯基问题解的唯一性和连续性。为了将 LYZ 的重要工作（定理 A）扩展到一般凸体的情况，我们建立了一些新的 Minkowski 型不等式，这些不等式与 $L_p$ 对偶 Minkowski 问题相关的优化问题密切相关。当 $q< p$ 时，得到了一般凸体的 $L_p$ 对偶 Minkowski 问题解的唯一性。此外，我们还得到了凸体的$L_p$ dual Minkowski 问题解的连续性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.