一些高维逆 Bonnesen 型不等式

数学物理学报 ›› 2023, Vol. 43 ›› Issue (4): 985-993.

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一些高维逆 Bonnesen 型不等式

王贺军()

山东师范大学数学与统计学院济南 250358

收稿日期:2022-01-14 修回日期:2023-02-06 出版日期:2023-08-26 发布日期:2023-07-03
通讯作者: 王贺军 E-mail:wanghjmath@sdnu.edu.cn
基金资助:
中国博士后科学基金(2020M682222);山东省自然科学基金(ZR2020QA003);山东省自然科学基金(ZR2020QA004)

Some Reverse Bonnesen-style Inequalities in $n$-Dimensional Euclidean Space $\mathbb{R} ^n$

Wang Hejun()

School of Mathematics and Statistics, Shandong Normal University, Ji'nan 250358

Received:2022-01-14 Revised:2023-02-06 Online:2023-08-26 Published:2023-07-03
Contact: Hejun Wang E-mail:wanghjmath@sdnu.edu.cn
Supported by:
China Postdoctoral Science Foundation(2020M682222);Natural Science Foundation of Shandong Province(ZR2020QA003);Natural Science Foundation of Shandong Province(ZR2020QA004)

摘要/Abstract

摘要：

该文研究 $n$ 维欧氏空间 $\mathbb{R} ^n$ 中逆 Bonnesen 型不等式, 主要利用 Urysohn 不等式, 对偶等周不等式, 平均宽度与平均截面面积, 得到了一些高维逆 Bonnesen 型不等式.

关键词: 逆 Bonnesen 型不等式, 等周亏格, 平均宽度, 平均截面面积.

Abstract:

This paper mainly studies reverse Bonnesen-style inequalities in $n$-dimensional Euclidean space $\mathbb{R} ^n$. By the Urysohn inequality, the dual isoperimetric inequality, mean width and mean intersection area, some new reverse Bonnesen-style inequalities for general convex bodies are obtained in $\mathbb{R} ^n$.

Key words: Reverse Bonnesen-style inequality, Isoperimetric deficit, Mean width, Mean intersection area

中图分类号:

O186.5

王贺军. 一些高维逆 Bonnesen 型不等式[J]. 数学物理学报, 2023, 43(4): 985-993.

Wang Hejun. Some Reverse Bonnesen-style Inequalities in $n$-Dimensional Euclidean Space $\mathbb{R} ^n$[J]. Acta mathematica scientia,Series A, 2023, 43(4): 985-993.

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一些高维逆 Bonnesen 型不等式

Some Reverse Bonnesen-style Inequalities in $n$-Dimensional Euclidean Space $\mathbb{R} ^n$

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