| 凸体的曲率映象与仿射表面积 |
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| 引用本文： | 冷岗松.凸体的曲率映象与仿射表面积[J].数学学报,2002,45(4):797-802. |
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| 作者姓名： | 冷岗松 |
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| 作者单位： | 湖南师范大学数学系,湖南,长沙410006;上海大学数学系,上海,200436 |
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| 基金项目： | 中国博士后基金资助项目，上海市教委发展基金资助项目 |
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| 摘 要： | 本文研究了一些特殊凸体与其极体的曲率仿射表面积乘积的下界.对任意两个凸体,建立了它们的投影体的混合体积与其仿射表面积的一个不等式（见文1-15]）.
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| 关 键 词： | 凸体 曲率映象 仿射表面积 混合体积 不等式 |
| 文章编号： | 0583-1431(2002)04-0797-06 |
| 修稿时间： | 1999年9月23日 |
Affine Surface Areas of Curvature Images for Convex Bodies |
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| Gang Song LENG.Affine Surface Areas of Curvature Images for Convex Bodies[J].Acta Mathematica Sinica,2002,45(4):797-802. |
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| Authors: | Gang Song LENG |
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| Institution: | Gang Song LENG(Department of Mathematics, Hunan Normal University, Changsha 410006, P. R. China)(Department of Mathematics, Shanghai University, Shanghai 200436, P. R. China)(E-mail: lenggangsong@chinaren. com) |
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| Abstract: | In this paper, we give a lower bound of the volume product for simplices, and prove that the Santalo point of a simplex is identical with its centroid. Some inequalities have been established for the affine surface areas of the curvature images of simplices, zonoid and centrally symmetric convex bodies. Further, we prove an inequality for the mixed volumes and surface areas of projection bodies (see 1-15]). |
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| Keywords: | Convex bodies Curvature images Surface areas Mixed volumes Inequalities |
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