平面凸体的Wulff曲率积分不等式  

Integral inequality of Wulff curvature for plane convex bodies

作　　者：王亚玲 董旭 曾春娜 Yaling WANG;Xu DONG;Chunna ZENG(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《山东大学学报（理学版）》2024年第8期113-117,126,共6页Journal of Shandong University(Natural Science)

基　　金：重庆英才青年拔尖计划资助项目(CQYC2021059145);重庆市研究生科研创新资助项目(CYS23412);重庆市教育委员会科学技术研究项目(KJQN201900530,KJZD-K202200509)

摘　　要：本文主要研究平面上Wulff流情形下的Wulff曲率积分不等式。利用Green-Osher不等式和Wulff-Steiner多项式获得了对称与非对称凸体的任意次幂的Wulff曲率积分不等式。特别地,当其中一凸体为单位圆时,获得了平面凸曲线任意次幂的曲率积分不等式。In this paper,we mainly study the integral inequality of Wulff curvature in the case of Wulff flow on the plane.By using Green-Osher inequality and Wulff-Steiner polynomials,we obtain the Wulff curvature integral inequality of any power of symmetric and nonsymmetric convex bodies.Specifically,when one of the convex bodies is an unit circle,the curvature integral inequality of any powers of the plane convex curve is obtained.

关 键 词：凸体 Steiner多项式 Green-Osher不等式 Wulff曲率 Wulff-Steiner多项式 

分 类 号：O186.5[理学—数学]