$\mathbb{R}^3$中四面体的Bonnesen型等周不等式

Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (2): 296-302.

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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)

Abstract

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

CLC Number:

O186.5

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

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