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Mathematics 2019, 7(4), 343; https://doi.org/10.3390/math7040343

Lp Radial Blaschke-Minkowski Homomorphisms and Lp Dual Affine Surface Areas

1
Department of Mathematics, China Three Gorges University, Yichang 443002, China
2
Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, China
*
Author to whom correspondence should be addressed.
Received: 17 February 2019 / Revised: 2 April 2019 / Accepted: 3 April 2019 / Published: 10 April 2019
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PDF [267 KB, uploaded 10 April 2019]

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. View Full-Text
Keywords: Busemann-Petty problem; Lp radial Blaschke-Minkowski homomorphism; Lp dual affine surface area; Brunn-Minkowski inequality Busemann-Petty problem; Lp radial Blaschke-Minkowski homomorphism; Lp dual affine surface area; Brunn-Minkowski inequality
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Shen, Z.; Wang, W. Lp Radial Blaschke-Minkowski Homomorphisms and Lp Dual Affine Surface Areas. Mathematics 2019, 7, 343.

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