摘要
给出Brunn-Minkowski面积不等式的两种特殊证明方法.首先描述面积、周长及混合面积的傅里叶级数表示法,再介绍一个内积空间及一个有关实数不等式的引理,把傅里叶级数表达式带入实数不等式中并利用内积算法得到结论;再把Minkowski和的定义推广到一般情形,把面积、周长表示为t的函数,利用函数的凹凸性证明了Brunn-Minkowski面积不等式.
Give two special proofs of area Brunn-Minkowski inequality.Firstly describe the representations of Fourier series for area,perimeter and mixed area,then give a lemma of four real numbers and the inner-product sequence space,and put the representations of the Fourier series into the formula of the lemma and the inner-product,and come to the conclusion.Finally use the improved Minkowski sum of convex bodies,define the area and perimeter with argument t,then apply the convexity of A(t)/L(t)to come the result too.
作者
汪小玉
何梅
WANG Xiao-yu;HE Mei(School of Mathematical and Statics,Hefei Normal University,Hefei Anhui 230601,China;School of Mathematical and Statics,Huaiyin Normal University,Huaian Jiangsu 223300,China)
出处
《淮阴师范学院学报（自然科学版）》
CAS
2020年第4期293-297,共5页
Journal of Huaiyin Teachers College;Natural Science Edition
