平面上的新凸体与逆Bonnesen-型不等式  

On New Convex Bodies and Reverse Bonnesen-Style,Inequalities in the Plane

作　　者：张增乐 罗淼[1,2] 陈方维[3] 

机构地区：[1]西南大学数学与统计学院,重庆400715 [2]贵州师范大学数学与计算机科学学院,贵阳550001 [3]贵州财经大学数学与统计学院,贵阳550025

出　　处：《西南师范大学学报（自然科学版）》2015年第4期27-30,共4页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：贵州省科学技术基金项目(黔科合J字LKS[2011]16);国家自然科学基金项目(11401486;11161007)

摘　　要：利用给定凸体的支持函数构造出3类新凸体.通过讨论前两类新凸体的几何性质,得到了一些逆Bonnesen-型不等式.通过讨论后一类新凸体,给出了新凸体由给定凸体变化为圆盘的过程,且在该变化过程中,新凸体的周长不变,面积不减.In this paper ,we have constructed three new classes of convex bodies by the support function of the given convex body .By discussing the geometric properties of the first two classes of convex bodies ,we have obtained some reverse Bonnesen-style inequalities .Via discussing the last class of convex bodies ,we give the process that the given convex body changes a disk ,and the perimeter of the new convex body has not changed ,the are of the new convex body has not decreased in the process .

关 键 词：凸体 支持函数 新凸体 等周不等式 逆Bonnesen-型不等式 

分 类 号：O186.5[理学—数学]