$\mathbb{R}^n$中的广义逆Bonnesen型不等式

数学物理学报 ›› 2022, Vol. 42 ›› Issue (3): 641-650.

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$\mathbb{R}^n$中的广义逆Bonnesen型不等式

董旭¹(),张燕¹(),曾春娜^1,*(),王星星²()

¹ 重庆师范大学数学科学学院重庆 401331
² 上海立信会计金融学院统计与数学学院上海 201620

收稿日期:2021-08-04 出版日期:2022-06-26 发布日期:2022-05-09
通讯作者: 曾春娜 E-mail:2931574183@qq.com;zengchn@163.com;2279282928@qq.com;m13098792429@163.com
作者简介:董旭, E-mail: 2931574183@qq.com|张燕, E-mail: zengchn@163.com|王星星, E-mail: m13098792429@163.com
基金资助:
国家自然科学基金(11801048);重庆英才青年拔尖计划(CQYC2021059145);重庆市自然科学基金(cstc2020jcyj-msxmX0609);重庆市留学人员创新创业支持计划(cx2018034);重庆市留学人员创新创业支持计划(cx2019155);重庆市教育委员会科学技术研究项目(KJQN201900530)

The General Inverse Bonnesen-Style Inequalities in $\mathbb{R}^n$

Xu Dong¹(),Yan Zhang¹(),Chunna Zeng^1,*(),Xingxing Wang²()

¹ School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331
² School of Mathematics and Statistics, Shanghai Lixin University of Accounting and Finance, Shanghai 201620

Received:2021-08-04 Online:2022-06-26 Published:2022-05-09
Contact: Chunna Zeng E-mail:2931574183@qq.com;zengchn@163.com;2279282928@qq.com;m13098792429@163.com
Supported by:
the NSFC(11801048);the Young Top-Talent Program of Chongqing(CQYC2021059145);the NSF of Chongqing(cstc2020jcyj-msxmX0609);the Venture Innovation Support Program for Chongqing Overseas Returnees(cx2018034);the Venture Innovation Support Program for Chongqing Overseas Returnees(cx2019155);the Technology Research Foundation of Chongqing Educational Committee(KJQN201900530)

摘要/Abstract

摘要：

等周问题在积分几何中具有举足轻重的地位. 该文主要研究$\mathbb{R}^n$中等周不等式的逆形式, 即广义逆Bonnesen型不等式. 该文获得了$\mathbb{R}^n$中几个新广义等周亏格上界的结果, 作为推论, 得到了更一般的平面上的逆Bonnesen型不等式; 最后给出其中三个上界结果之间的最佳估计.

关键词: Aleksandrov-Fenchel不等式, 相对均质积分, 逆Bonnesen型不等式

Abstract:

The isoperimetric problem plays an important role in integral geometry. In this paper we mainly investigate the inverse form of the isoperimetric inequality, i.e. the general inverse Bonnesen-type inequalities. The upper bounds of several new general isoperimetric genus are obtained. Futhermore, as corollaries, we get a series of classical inverse Bonnesen-type inequalities in the plane. Finally, the best estimate between the results of three upper bounds is given.

Key words: Aleksandrov-fenchel inequalities, Inverse Bonnesen type inequality, Quermassintegrals

中图分类号:

O186.5

董旭,张燕,曾春娜,王星星. $\mathbb{R}^n$中的广义逆Bonnesen型不等式[J]. 数学物理学报, 2022, 42(3): 641-650.

Xu Dong,Yan Zhang,Chunna Zeng,Xingxing Wang. The General Inverse Bonnesen-Style Inequalities in $\mathbb{R}^n$[J]. Acta mathematica scientia,Series A, 2022, 42(3): 641-650.

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$\mathbb{R}^n$中的广义逆Bonnesen型不等式

The General Inverse Bonnesen-Style Inequalities in $\mathbb{R}^n$

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