L p Radial Blaschke-Minkowski Homomorphisms and L p Dual Affine Surface Areas

Zhonghuan Shen and Weidong Wang
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Zhonghuan Shen: Department of Mathematics, China Three Gorges University, Yichang 443002, China
Weidong Wang: Department of Mathematics, China Three Gorges University, Yichang 443002, China

Mathematics, 2019, vol. 7, issue 4, 1-14

Abstract: Schuster introduced the notion of radial Blaschke-Minkowski homomorphism and considered the Busemann-Petty problem for volume forms. Whereafter, Wang, Liu and He presented the L p radial Blaschke-Minkowski homomorphisms and extended Schuster’s results. In this paper, associated with L p dual affine surface areas, we give an affirmative and a negative form of the Busemann-Petty problem and establish two Brunn-Minkowski inequalities for the L p radial Blaschke-Minkowski homomorphisms.

Keywords: Busemann-Petty problem; L p radial Blaschke-Minkowski homomorphism; L p dual affine surface area; Brunn-Minkowski inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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