两混合凸体的相对曲率积分不等式  

The Relative Curvature Integral Inequalities of Two Mixed Convex Bodies

作　　者：董旭 王亚玲 周玉奇 曾春娜 Xu DONG;Ya Ling WANG;Yu Qi ZHOU;Chun Na ZENG(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,P.R.China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《数学学报（中文版）》2024年第4期732-742,共11页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金重大专项(12141101);重庆英才青年拔尖计划(CQYC2021059145);重庆市高校创新研究群体项目(CXQT21014);重庆市研究生科研创新项目(CYS22556);重庆市教育委员会科学技术研究项目(KJZD-K202200509)。

摘　　要：曲率积分不等式在几何不等式中有举足轻重的地位.本文主要利用非对称的Green-Osher不等式,获得了两混合凸体高次幂的相对曲率积分界的估计.这些不等式在Green和Osher工作的基础上去掉了对称性条件,为著名的Green-Osher不等式的改进形式.特别地,当一个凸体为单位圆时,获得了R^(2)中的Ros不等式、曲率熵不等式,提供了曲率熵不等式新的简化证明.The curvature integral inequalities are important in geometric inequalities.In this paper,by using the nonsymmetric Green—Osher inequality,we obtain the bounds of the relative curvature integral of the higher power of two mixed convex bodies.On the basis of Green and Osher's work,these results remove the symmetric condition and are the famous strengthened form of Green—Osher inequality.In particular,when a convex body is a unit circle,we obtain the Ros inequality and the inequalities of curvature entropy in R^(2).And the new simplified proofs of the inequalities of curvature entropy are provided.

关 键 词：Gage等周不等式 Ros不等式 Green-Osher不等式 曲率熵不等式 

分 类 号：O186.5[理学—数学]