Wulff-Gage等周不等式的分析形式  

Analytical Form of Wulff-Gage's Isoperimetric Inequality

作　　者：马磊 MA Lei(School of Sciences,Guangdong Preschool Normal College in Maoming,Maoming 525200,China)

机构地区：[1]广东茂名幼儿师范专科学校理学院,广东茂名525200

出　　处：《广东石油化工学院学报》2025年第1期122-126,共5页Journal of Guangdong University of Petrochemical Technology

基　　金：广东省普通高校特色创新项目(2023KTSCX381);茂名市科技计划项目(2023390)。

摘　　要：文章研究了Gage等周不等式与Wulff-Gage等周不等式的分析形式。利用函数积分不等式、周期函数的性质及Cauchy-Buniakowsky-Schwarz不等式,得到了偶的(对称的)Wulff-Gage等周不等式的分析形式,其特殊形式即为偶的(对称的) Gage等周不等式的分析形式。相当于为关于原点对称且具有光滑边界的闭凸区域的Wulff-Gage等周不等式与Gage等周不等式,提供了一种纯分析形式的证明。The analytical forms of Gage's isoperimetric inequality and Wulff-Gage's isoperimetric inequality is investigated.Based on the integral inequality of functions,the properties of periodic functions,and Cauchy Buniakowsky Schwarz,the even(symmetric)Wulff-Gage's isoperimetric inequality are obtained,and its special form is the analytical form of the even(symmetric)Gage's isoperimetric inequality.This means that a pure analytical proof has been found for the Wulff-Gage's isoperimetric inequality and Gage's isoperimetric inequality for closed convex domains with symmetric origins and smooth boundaries.

关 键 词：Wulff-Gage等周不等式 Gage等周不等式 简单闭凸曲线 支撑函数 

分 类 号：O186.5[理学—数学]