The Busemann–Petty problem for Lp-mixed radial Blaschke–Minkowski homomorphisms

Bin Chen; Weidong Wang; Peibiao Zhao

doi:10.1216/rmj-2021-51-1195

Abstract

In this paper, we introduce the concept of ${L_{p}}$ -mixed radial Blaschke–Minkowski homomorphisms for star bodies. Further, associated with dual quermassintegrals, we give an affirmative answer and two negative answers of the Busemann–Petty problem for the ${L_{p}}$ -mixed radial Blaschke–Minkowski homomorphisms.

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Bin Chen. Weidong Wang. Peibiao Zhao. "The Busemann–Petty problem for ${L_{p}}$ -mixed radial Blaschke–Minkowski homomorphisms." Rocky Mountain J. Math. 51 (4) 1195 - 1208, August 2021. https://doi.org/10.1216/rmj.2021.51.1195

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Received: 25 February 2020; Revised: 10 December 2020; Accepted: 30 December 2020; Published: August 2021

First available in Project Euclid: 5 August 2021

MathSciNet: MR4298840

zbMATH: 1478.52001

Digital Object Identifier: 10.1216/rmj.2021.51.1195

Subjects:

Primary: 52A20 , 52A39 , 52A40

Keywords: Busemann–Petty problem , dual quermassintegral , Lp-mixed radial Blaschke–Minkowski homomorphism , star body

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