| 投影体的宽度积分和仿射表面积 |
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| 引用本文： | 赵长健,冷岗松.投影体的宽度积分和仿射表面积[J].数学年刊A辑(中文版),2005(2). |
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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 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(N0．200203)资助的项目． |
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| 摘 要： | 本文运用凸几何分析理论,建立了投影体的宽度积分和仿射表面积的一些新型Brunn-Minkowski 不等式,这些结果改进了Lutwak的几个有用的定理.作为应用,进一步给出了混合投影体极的Brunn- Minkowski型不等式.
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| 关 键 词： | 凸体的宽度积分 仿射表面积 投影体的极 投影体的宽度积分 |
WIDTH-INTEGRALS OF PROJECTION BODIES AND AFFINE SURFACE AREA |
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| ZHAO Changjian LENG Gangsong.WIDTH-INTEGRALS OF PROJECTION BODIES AND AFFINE SURFACE AREA[J].Chinese Annals of Mathematics,2005(2). |
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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,Shanghai University,Shanghai 200444,China. |
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| Abstract: | This paper establishes some new Brunn-Minkowski type inequalities for width-integrals of projection bodies and affine surface area by using convex geometric analysis theory, which improve Lutwak's several important theorems. As application, the Brunn-Minkowski inequality for polars of mixed projection bodies is obtained. |
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| Keywords: | Width-integrals of convex body Affine surface area Polars of projection body Width-integral of projection body |
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