$\mathbb{R}^3$中四面体的Bonnesen型等周不等式

数学物理学报 ›› 2021, Vol. 41 ›› Issue (2): 296-302.

$\mathbb{R}^3$中四面体的Bonnesen型等周不等式

曾春娜¹(),彭璐¹(),马磊²(),王星星^3,*()

¹ 重庆师范大学数学科学学院重庆 401331
² 广东茂名幼儿师范专科学校广东茂名 525000
³ 上海立信会计金融学院统计与数学学院上海 201620

收稿日期:2020-01-07 出版日期:2021-04-26 发布日期:2021-04-29
通讯作者: 王星星 E-mail:zengchn@163.com;cqkx95@163.com;maleiyou@163.com;m13098792429@163.com
作者简介:曾春娜, E-mail: zengchn@163.com|彭璐, E-mail: cqkx95@163.com|马磊, E-mail: maleiyou@163.com
基金资助:
国家自然科学基金(11801048);重庆市自然科学基金(cstc2020jcyj-msxmX0609);重庆市教育委员会科学技术研究项目(KJQN201900530);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);广东省普通高校特色创新项(2020KTSCX358)

The Bonnesen-Style Isoperimetric Inequalities of the Tetrahedral in $\mathbb{R}^3$

Chunna Zeng¹(),Lu Peng¹(),Lei Ma²(),Xinxin Wang^3,*()

¹ School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331
² Department of Education, Maoming Infant Teachers College, Guangdong Maoming 525000
³ School of Mathematics and Statistics, Shanghai Lixin University of Accounting and Finance, Shanghai 201620

Received:2020-01-07 Online:2021-04-26 Published:2021-04-29
Contact: Xinxin Wang E-mail:zengchn@163.com;cqkx95@163.com;maleiyou@163.com;m13098792429@163.com
Supported by:
the NSFC(11801048);the NSF of Chongqing(cstc2020jcyj-msxmX0609);the Technology Research Foundation of Chongqing Educational Committee(KJQN201900530);the Venture & Innovation Support Program for Chongqing Overseas Returnees(cx2018034);the Venture & Innovation Support Program for Chongqing Overseas Returnees(cx2019155);the Characteristic Innovation Project of Guangdong Universities(2020KTSCX358)

摘要/Abstract

摘要：

该文主要研究$\mathbb{R}^3$中四面体的Bonnesen型与逆Bonnesen型等周不等式.对于$\mathbb{R}^3$中给定的四面体，利用其表面积、体积、内切球半径及外接球半径之间的关系，构造出两个重要的几何不等式，得到了四面体的一些Bonnesen型等周不等式与等周不等式的新的简单证明.更进一步地，通过讨论四面体等周亏格的上界估计，获得了两个用内切球半径与外接球半径表示的逆Bonnesen型等周不等式.

关键词: 四面体, Bonnesen型不等式, 逆Bonnesen型等周不等式

Abstract:

This paper mainly studies Bonnesen-type isoperimetric inequalities and reverse Bonnesen-type isoperimetric inequalities of tetrahedron in $\mathbb{R}^3$. For a given tetrahedron in $\mathbb{R}^3$, by appling the relations of the surface area, volume, radius of inscribed sphere and radius of circumscribed radius, two important geometric inequalities are constructed, some Bonnesen-type isoperimetric inequalities of tetrahedron are obatainand, and a new simple proof of isoperimetric inequality of tetrahedron is achieved. Furthermore, by using the upper bound estimates of the isoperimetric deficit of tetrahedral, we obtain two reverse Bonnesen-type isoperimetric inequalities of tetrahedron of the expressions radius of inscribed sphere and radius of circumscribed radius.

Key words: Tetrahedron, Bonnesen-type isoperimetric inequality, Reverse Bonnesen-type isoperimetric inequality

中图分类号:

O186.5

曾春娜,彭璐,马磊,王星星. $\mathbb{R}^3$中四面体的Bonnesen型等周不等式[J]. 数学物理学报, 2021, 41(2): 296-302.

Chunna Zeng,Lu Peng,Lei Ma,Xinxin Wang. The Bonnesen-Style Isoperimetric Inequalities of the Tetrahedral in $\mathbb{R}^3$[J]. Acta mathematica scientia,Series A, 2021, 41(2): 296-302.

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