| 不变的赋值函数与Cauchy投影公式(英文) |
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| 引用本文： | 陈方维,杨丛丽.不变的赋值函数与Cauchy投影公式(英文)[J].数学杂志,2012,32(2):217-223. |
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| 作者姓名： | 陈方维 杨丛丽 |
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| 作者单位： | 1. 贵州财经学学院数学与统计分院,贵州贵阳,550004
2. 贵州师范大学数学与计算机科学学院,贵州贵阳550001;Dept.of Physics and Mathematics,Joensuu Campus,Yliopistokatu(Z),P.O.Box 111 FI-80101 Joensuu,University of Eastern Finland, Finland |
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| 基金项目： | Supported by Guizhou Fundation for Science and Technology ([2010]2242) |
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| 摘 要： | 本文研究了Rn中凸集上不变的赋值函数与凸体的投影问题.利用赋值函数的方法,我们获得了凸体在任意维平面上投影的Cauchy公式和Kubota公式,这些结果推广了经典的Cauchy公式和Kubota公式.
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| 关 键 词： | 赋值函数 内蕴体积 均值积分 Cauchy公式 Kubota公式 |
ON INVARIANT VALUATIONS AND THE CAUCHY FORMULA |
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| CHEN Fang-wei
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YANG Cong-li.ON INVARIANT VALUATIONS AND THE CAUCHY FORMULA[J].Journal of Mathematics,2012,32(2):217-223. |
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| Authors: | CHEN Fang-wei YANG Cong-li |
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| Institution: | 2,3(1.Dept.of Math.and Statistics,Guizhou College of Finance and Economics,Guiyang 550004,China)(2.School of Math.and Computer Science,Guizhou Normal University,Guiyang 550001,China)(3.Dept.of Physics and Mathematics,Joensuu Campus,Yliopistokatu 7,P.O.Box 111 FI-80101 Joensuu,University of Eastern Finland,Finland) |
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| Abstract: | In this paper,we investigate the invariant valuations and the projection of convex bodies of Rn.By using the method of valuations defined on convex bodies,we obtain the generalized Cauchy formula and the generalized Kubota formula for convex bodies.These results extend the classical Cauchy formula and Kubota formula. |
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| Keywords: | valuation intrinsic volume quermassintegral Cauchy formula Kubota formula |
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