| L_p混合质心体均质积分和对偶均质积分Brunn-Minkowski不等式（英文） |
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| 引用本文： | 马统一,刘春燕.L_p混合质心体均质积分和对偶均质积分Brunn-Minkowski不等式（英文）[J].吉首大学学报(自然科学版),2011,32(4):15-25. |
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| 作者姓名： | 马统一 刘春燕 |
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| 作者单位： | (1.河西学院数学与统计学院,甘肃 张掖 734000；2.西北师范大学数学与信息科学学院,甘肃 兰州 730070) |
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| 基金项目： | National Natural Science Foundation of China(10971128); Foundation of the Education Department of Gansu Province(2009B-09) |
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| 摘 要： | 定义了新几何体Γ-p,iK和Lp混合调和Blaschke加K＋¨pL的概念,建立了Lp混合质心体Γp,iK的均质积分和对偶均质积分的Brunn-Minkowski不等式,并研究了算子Γp,i和Γ-p,i的单调性.
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| 关 键 词： | Lp质心体 Lp混合质心体 Lp混合投影体 均质积分 对偶均质积分 Lp混合调和Blaschke加 |
On Brunn-Minkowski Inequality for the Quermassintegrals and Dual Quermassintegrals of L_p-Mixed Centroid Bodies |
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| MA Tong-yi,LIU Chun-yan.On Brunn-Minkowski Inequality for the Quermassintegrals and Dual Quermassintegrals of L_p-Mixed Centroid Bodies[J].Journal of Jishou University(Natural Science Edition),2011,32(4):15-25. |
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| Authors: | MA Tong-yi LIU Chun-yan |
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| Institution: | (1.College of Mathematics and Statistics Science,Hexi University,Zhangye 734000,Gansu China;2.College of Mathematics and Information Science,Northwest Normal University,Lanzhou 730070,China ) |
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| Abstract: | The notions of new geometric body Γ-p,iK and Lp-mixed harmonic Blaschke add k＋pL are defined.The Brunn-Minkowski inequalities for the quermassintegrals and dual quermassintegrals of Lp-mixed centroid body Γp,iK and its polar body associated with Lp-mixed harmonic Blaschke add are established,and the monotonicity of operator Γp,i and Γ-p,i is proved. |
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| Keywords: | Lp-centroid body Lp-mixed centroid body Lp-mixed projection body quermassintegrals dual quermassintegrals Lp-mixed harmonic Blaschke add |
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