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- W3016776276 abstract "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 <i>L<sub>p</sub></i> 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 <i>L<sub>p</sub></i> harmonic radial sum and <i>L<sub>p</sub></i> radial Blaschke sum, respectively." @default.
- W3016776276 created "2020-04-24" @default.
- W3016776276 creator A5071615222 @default.
- W3016776276 date "2020-01-01" @default.
- W3016776276 modified "2023-10-18" @default.
- W3016776276 title "Inequalities for the Mixed Radial Blaschke-Minkowski Homomorphisms and the Applications" @default.
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- W3016776276 doi "https://doi.org/10.11648/j.acm.20200901.12" @default.
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