引用本文:周媛, 张增乐.平面上的逆Bonnesen型Minkowski不等式[J].西南大学学报(自然科学版),2019,41(2):70~74
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平面上的逆Bonnesen型Minkowski不等式
周媛, 张增乐1,2
1. 西南大学 数学与统计学院, 重庆 400715;2. 重庆文理学院 数学与财经学院, 重庆 永川 402160
摘要:
研究了平面中形如AK,L2-AKALUK,L的Minkowski不等式的上界,即逆Bonnesen-型Minkowski不等式.设K,L是平面中的凸体,其面积分别为AKAL,其中AK,L为两凸体的混合面积,UK,L为与K,L有关的几何不变量.利用平面上给定两凸体的支持函数,构造一类与给定凸体相关的新凸体.通过对新凸体几何性质的讨论,得到了一些新的加强的逆Bonnesen-型Minkowski不等式,并用此类不等式可推出一些已有结果.
关键词:  凸体  支持函数  Minkowski不等式  逆Bonnesen-型Minkowski不等式
DOI:10.13718/j.cnki.xdzk.2019.02.011
分类号:O186.5
基金项目:国家自然科学基金项目(11671325).
Reverse Bonnesen-Style Minkowski Inequalities in the Plane
ZHOU Yuan, ZHANG Zeng-le1,2
1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China;2. School of Mathematics and Finance, Chongqing University of Arts and Sciences, Yongchuan Chongqing 402160, China
Abstract:
We study in this paper the upper bound of the Minkowski inequality in the plane, i.e. a reverse Bonnesen-style Minkowski inequality, such as AK,L2-AKALUK,L. Let K and L be convex bodies whose areas are AK and AL, respectively, and AK,L is the mixes area of the two convex bodies and UK,L is the geometric invariant related to K and L. We construct a class of convex body by the support function of the given convex bodies. By discussing the geometric properties of the new convex body, we obtain some new stronger reverse Bonnesen-style Minkowski inequalities and some results can be derived from those inequalities.
Key words:  convex body  support function  Minkowski inequality  reverse Bonnesen-style Minkowski inequality
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