弦长积分的极限性质与不等式

数学物理学报 ›› 2018, Vol. 38 ›› Issue (6): 1049-1057.

弦长积分的极限性质与不等式

曾春娜¹(),李冉²(),朱保成^3,*()

¹ 重庆师范大学数学科学学院重庆 401331
² 山东大学附中实验学校山东菏泽 404100
³ 湖北民族大学数学系湖北恩施 445000

收稿日期:2017-09-20 出版日期:2018-12-26 发布日期:2018-12-27
通讯作者: 朱保成 E-mail:zengchn@163.com;lizhunran@163.com;zhubaocheng814@163.com
作者简介:曾春娜, E-mail:zengchn@163.com|李冉, E-mail:lizhunran@163.com
基金资助:
国家自然科学基金(11501185);国家自然科学基金(11801048);重庆市基础科学与前沿技术研究专项(cstc2017jcyjAX0022);重庆市留学人员回国创业创新支持计划(cx2018034)

Some Properties and Inequalities for Chord-Integrals of Star Bodies

Chunna Zeng¹(),Ran Li²(),Baocheng Zhu^3,*()

¹ School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331
² SDFZ Experimental School, Shandong Heze 404100
³ Department of Mathematics, Hubei University for Nationalities, Hubei Enshi 445000

Received:2017-09-20 Online:2018-12-26 Published:2018-12-27
Contact: Baocheng Zhu E-mail:zengchn@163.com;lizhunran@163.com;zhubaocheng814@163.com
Supported by:
Supported by the NSFC(11501185);Supported by the NSFC(11801048);the Chongqing Basic Science and Frontier Technology Research Project(cstc2017jcyjAX0022);the Venture & Innovation Support Program for Chongqing Overseas Returnees(cx2018034)

摘要/Abstract

摘要：

该文获得了$\mathbb{R}$ⁿ中星体弦长积分的一些极限性质，建立了星体弦长积分的不等式，包括弦长积分和对偶均质积分之间的不等式以及对偶Blaschke-Santaló不等式.

关键词: 凸体, 星体, 宽度积分, 弦长积分

Abstract:

In this paper, we obtain some limit properties of chord-integrals in $\mathbb{R}$ⁿ, and establish some inequalities for chord-integrals of star bodies, including the inequalities between chord-integrals and dual quermass-integrals, the dual Blaschke-Santaló inequality and so on.

Key words: Convex bodies, Star bodies, Width-integrals, Chord-integrals

中图分类号:

O186.5

曾春娜,李冉,朱保成. 弦长积分的极限性质与不等式[J]. 数学物理学报, 2018, 38(6): 1049-1057.

Chunna Zeng,Ran Li,Baocheng Zhu. Some Properties and Inequalities for Chord-Integrals of Star Bodies[J]. Acta mathematica scientia,Series A, 2018, 38(6): 1049-1057.

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