| 一些几何不等式的等价关系 |
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| 引用本文： | 袁淑峰,金海林. 一些几何不等式的等价关系[J]. 上海大学学报(自然科学版), 2015, 21(6): 725-731. DOI: 10.3969/j.issn.1007-2861.2014.01.043 |
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| 作者姓名： | 袁淑峰 金海林 |
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| 作者单位： | (1. 上海大学理学院, 上海200444;2. 绍兴文理学院上虞分院, 浙江上虞312300) |
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| 基金项目： | 国家自然科学基金资助项目(11271244); 浙江省教育厅科研基金资助项目(Y201328555) |
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| 摘 要： | Brunn-Minkowski不等式和Minkowski不等式是凸几何中的两个重要而基本的不等式. 近期, 已有学者得到了这两个不等式的Orlicz版本, 从而构建起Orlicz-Brunn-Minkowski理论的框架. 本工作证明经典的Brunn-Minkowski不等式、Minkowski不等式、Orlicz-Brunn-Minkowski不等式和Orlicz-Minkowski不等式是等价的.
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| 关 键 词： | Brunn-Minkowski不等式 Minkowski不等式 Minkowski和 Orlicz和 均质积分 |
| 收稿时间： | 2014-03-04 |
Equivalence properties of some geometric inequalities |
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| YUAN Shu-Feng,JIN Hai-Lin. Equivalence properties of some geometric inequalities[J]. Journal of Shanghai University(Natural Science), 2015, 21(6): 725-731. DOI: 10.3969/j.issn.1007-2861.2014.01.043 |
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| Authors: | YUAN Shu-Feng JIN Hai-Lin |
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| Affiliation: | (1.College of Sciences, Shanghai University, Shanghai 200444, China;2. Shangyu Branch, Shaoxing University, Shangyu 312300, Zhejiang, China) |
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| Abstract: | Brunn-Minkowski inequality and Minkowski inequality are two important and fundamental inequalities in convex geometric analysis. Recently, some researchers established Orlicz extension of these two inequalities, and constructed a general framework for the Orlicz-Brunn-Minkowski theory. The purpose of this paper is to show equivalence properties of these four inequalities, i.e., classical Brunn-Minkowski inequality, classical Minkowski inequality, Orlicz-Brunn-Minkowski inequality and Orlicz-Minkowski inequality. |
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| Keywords: | Brunn-Minkowski inequality Minkowski addition Minkowski inequality Orlicz addition Quermassintegral |
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