Lp混合质心体均质积分和对偶均质积分Brunn-Minkowski不等式

journal6 ›› 2011, Vol. 32 ›› Issue (4): 15-25.

L_p混合质心体均质积分和对偶均质积分Brunn-Minkowski不等式

(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)

出版日期:2011-07-25 发布日期:2012-04-07

On Brunn-Minkowski Inequality for the Quermassintegrals and Dual Quermassintegrals of L_p-Mixed Centroid Bodies

(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 )

Online:2011-07-25 Published:2012-04-07
About author:MA Tong-yi(1959-),male,was born in Huining County,Gansu Province,professor of Hexi University;research area are convex geometric analysis and distance geometry study.
Supported by:
National Natural Science Foundation of China (10971128);Foundation of the Education Department of Gansu Province (2009B-09)

摘要/Abstract

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.

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

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.

Key words: Lp-centroid body, Lp-mixed centroid body, Lp-mixed projection body, quermassintegrals, dual quermassintegrals, Lp-mixed harmonic Blaschke add

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[J]. journal6, 2011, 32(4): 15-25.

MA Tong-Yi, LIU Chun-Yan. On Brunn-Minkowski Inequality for the Quermassintegrals and Dual Quermassintegrals of L_p-Mixed Centroid Bodies[J]. journal6, 2011, 32(4): 15-25.

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