R^(3)中四面体的Bonnesen型等周不等式  

The Bonnesen-Style Isoperimetric Inequalities of the Tetrahedral in R^(3)

作　　者：曾春娜 彭璐 马磊 王星星 Zeng Chunna;Peng Lu;Ma Lei;Wang Xinxin(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331;Department of Education,Maoming Infant Teachers College,Guangdong Maoming 525000;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]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

出　　处：《数学物理学报（A辑）》2021年第2期296-302,共7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,cx2019155);广东省普通高校特色创新项目(2020KTSCX358)。

摘　　要：该文主要研究R^(3)中四面体的Bonnesen型与逆Bonnesen型等周不等式.对于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.This paper mainly studies Bonnesen-type isoperimetric inequalities and reverse Bonnesen-type isoperimetric inequalities of tetrahedron in R^(3).For a given tetrahedron in 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.

关 键 词：四面体 BONNESEN型不等式 逆Bonnesen型等周不等式 

分 类 号：O186.5[理学—数学]