Inequalities for the Mixed Radial Blaschke-Minkowski Homomorphisms and the Applications
Applied and Computational Mathematics
Volume 9, Issue 1, February 2020, Pages: 14-19
Received: Dec. 8, 2019; Accepted: Dec. 19, 2019; Published: Apr. 17, 2020
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Weidong Wang, Department of Mathematics, China Three Gorges University, Yichang, China; Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, China
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The notion of intersection body is introduced by Lutwak in 1988, it is one of important research contents and led to the studies of Busemann-Petty problem in the Brunn-Minkowski theory. Based on the properties of the intersection bodies, Schuster introduced the notion of radial Blaschke-Minkowski homomorphisms and proved a lot of related inequalities. In this paper, by applying the dual mixed volume theory and analytic inequalities, we first give a lower bound of the dual quermassintegrals for the mixed radial Blaschke-Minkowski homomorphisms. As its an application, we get a reverse form of the well-known Busemann intersection inequality. Further, a Brunn-Minkowski type inequality of the Lp radial Minkowski sum for the dual quermassintegrals of mixed radial Blaschke-Minkowski homomorphisms is established, and then the intersection body version of this Brunn-Minkowski type inequality is yielded. From this, we not only extend Schuster's related result but also obtain the Brunn-Minkowski type inequalities of Lp harmonic radial sum and Lp radial Blaschke sum, respectively.
Dual Quermassintegral, Intersection Body, Radial Blaschke-Minkowski Homomorphism, Busemann Intersection Inequality, Lp Radial Minkowski Sum
To cite this article
Weidong Wang, Inequalities for the Mixed Radial Blaschke-Minkowski Homomorphisms and the Applications, Applied and Computational Mathematics. Vol. 9, No. 1, 2020, pp. 14-19. doi: 10.11648/j.acm.20200901.12
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