$\mathbb{R}^3$中四面体的几个新Bonnesen型不等式

Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (4): 989-996.

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Some New Bonnesen-Type Inequalities of the Tetrahedron in $\mathbb{R}^3$

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:2020-09-09 Online:2021-08-26 Published:2021-08-09
Contact: Chunna Zeng E-mail:2279282928@qq.com;zengchn@163.com;m13098792429@163.com
Supported by:
the NSFC(11801048);the NSF of Chongqin(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)

Abstract

Abstract:

Discrete isoperimetric problems play an important role in integral geometry and convex geometry. The stability of isoperimetric deficit can be characterized by Bonnesen-type inequality and inverse Bonnesen-type inequality. In this paper, we study the Bonnesen-type inequality and the inverse Bonnesen-type inequality for Tetrahedra in $\mathbb{R}^3$. And we obtain several new Bonnesen-type inequalities for Tetrahedra. It provides a simplified proof which is different from the isoperimetric inequality for Tetrahedra in Sturm ^[15]; finally, four inverse Bonnesen-type inequalities in terms of the radius of the circumscribed sphere and the radius of the circumscribed sphere are obtained.

Key words: Tetrahedron, Isoperimetric deficit, Bonnesen-type inequality, Inverse Bonnesen-type inequality

CLC Number:

O186.5

Yan Zhang,Chunna Zeng,Xingxing Wang. Some New Bonnesen-Type Inequalities of the Tetrahedron in $\mathbb{R}^3$[J].Acta mathematica scientia,Series A, 2021, 41(4): 989-996.

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[1]	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.
[2]	ZHANG Hong, XU Wen-Xue, LI Ze-Qing. Remarks on the Isoperimetric Deficit of the Planar Isosceles Trapezoids of Constant Width [J]. Acta mathematica scientia,Series A, 2013, 33(6): 1162-1168.

Some New Bonnesen-Type Inequalities of the Tetrahedron in $\mathbb{R}^3$

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