R^(3)中四面体的几个新Bonnesen型不等式  

Some New Bonnesen-Type Inequalities of the Tetrahedron in R^(3)

作　　者：张燕 曾春娜 王星星 Zhang Yan;Zeng Chunna;Wang Xingxing(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331;School of Mathematics and Statistics,Shanghai Lixin University of Accounting and Finance,Shanghai 201620)

机构地区：[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

出　　处：《数学物理学报（A辑）》2021年第4期989-996,共8页Acta Mathematica Scientia

基　　金：国家自然科学基金(11801048);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,cx2019155);重庆市教育委员会科学技术研究项目(KJQN201900530)。

摘　　要：离散的等周问题在积分几何与凸几何中扮演着重要角色.等周亏格的稳定性可以由Bonnesen型不等式和逆Bonnesen型不等式来刻画.该文主要研究R^(3)中四面体的Bonnesen型不等式和逆Bonnesen型不等式,获得了四面体的几个新的Bonnesen型不等式,并提供了不同于Sturm[15]关于四面体的等周不等式的一种简化证明;最后获得了几个用四面体内切球半径以及外接球半径表示的逆Bonnesen型不等式.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 R3.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.

关 键 词：四面体 等周亏格 BONNESEN型不等式 逆Bonnesen型不等式 

分 类 号：O186.5[理学—数学]