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

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

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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)

Abstract

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

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

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