| Aleksandrov-Fenchel不等式及应用 |
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| 引用本文： | 赵长健,冷岗松.Aleksandrov-Fenchel不等式及应用[J].数学年刊A辑(中文版),2005(4). |
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| 作者姓名： | 赵长健 冷岗松 |
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| 作者单位： | 中国计量学院理学院信息与数学科学系，上海大学理学院数学系 杭州 310018 上海大学理学院数学系，上海 200444，上海 200444 |
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| 基金项目： | 国家自然科学基金(No．10271071)
山东省高校中青年学术骨干基金(No．200203)资助的项目． |
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| 摘 要： | 本文运用Aleksandrov-Fenchel不等式,首先推广了Lutwak,Bonnesen和Fenchel等建立的三个有用的定理,这三个定理在解决某些唯一性问题中扮演着重要角色.然后,把这些结果从一般的混合体积和投影体推广到混合投影体的极和混合仿射表面积上,获得了一些较理想的结果.
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| 关 键 词： | 凸体 投影体 投影体的极 对偶混合体积 Aleksandrov—Fenchel不等式 |
THE ALEKSANDROV-FENCHEL INEQUALITIES AND APPLICATIONS |
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| ZHAO Changjian LENG Gangsong.THE ALEKSANDROV-FENCHEL INEQUALITIES AND APPLICATIONS[J].Chinese Annals of Mathematics,2005(4). |
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| Authors: | ZHAO Changjian LENG Gangsong |
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| Institution: | ZHAO Changjian LENG Gangsong Department of Information and Mathematics Sciences,College of Science,China Institute of Metrology,Hangzhou 310018,China, Department of Mathematics,College of Science,Shanghai University,Shanghai 200444,China. Department of Mathematics,College of Science,Shanghai University,Shanghai 200444,China. |
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| Abstract: | By using the Aleksandrov-Fenchel inequalities, the authors first generalize Lutwak and Bonnesen-Fenchel's three important theorems which have been very valuable in answering a variety of uniqueness questions. Then, the authors improve above results from mixed volume and projection bodies to the polars of mixed projection bodies and affine surface area, and get some analogous results. |
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| Keywords: | Convex body Projection body Polar of projection body Dual mixed volume Aleksandrov-Fenchel inequality |
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