非对称的$L_{p}$-径向差体

齐继兵

doi:10.12066/j.issn.1007-2861.2032

上海大学学报(自然科学版) >

2019 , Vol. 25 >Issue 4: 493 - 501

DOI: https://doi.org/10.12066/j.issn.1007-2861.2032

研究论文

非对称的$L_{p}$-径向差体

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1.上海大学理学院,上海 200444
2. 合肥师范学院数学与统计学院, 合肥 230601

收稿日期: 2017-10-26

网络出版日期: 2019-09-04

基金资助

安徽省自然科学基金资助项目(1908085QA04)

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Asymmetric $L_{p}$-radial difference bodies

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1.College of Sciences, Shanghai University, Shanghai 200444
2. Department of Mathematics and Statistics, Hefei Normal University, Hefei 230601, China

Received date: 2017-10-26

Online published: 2019-09-04

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摘要

定义了关于星体的非对称的 $L_{p}$-径向差体, 研究了其性质, 建立了关于非对称 $L_{p}$-径向差体的对偶均值积分的几个不等式. 作为其特例, 得到非对称$L_{p}$-径向差体体积的几个不等式.

关键词： 星体; 差体; 均值积分; 凸几何

本文引用格式

齐继兵 . 非对称的$L_{p}$-径向差体[J]. 上海大学学报(自然科学版), 2019 , 25(4) : 493 -501 . DOI: 10.12066/j.issn.1007-2861.2032

Abstract

The notion of asymmetric $L_{p}$-radial difference bodies about star bodies has been defined, and some of their properties have been studied. Some inequalities for dual quermassintegrals of asymmetric $L_{p}$-radial difference bodies have been established. In particular, some inequalities for the volumes of asymmetric $L_p$-radial difference bodies have been obtained.

Key words： star body; difference bodies; dual quermassintegrals; convex geometry

参考文献

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