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Orlicz mixed radial Blaschke–Minkowski homomorphisms
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas ( IF 1.8 ) Pub Date : 2020-03-24 , DOI: 10.1007/s13398-020-00835-1
Chang-Jian Zhao , Wing Sum Cheung

Our main aim is to generalize the mixed radial Blaschke–Minkowski homomorphisms to the Orlicz space. By calculating first-order variation of the harmonic p -dual quermassintegrals of mixed radial Blaschke–Minkowski homomorphisms, we introduce a new affine geometric quantity and call it Orlicz mixed radial Blaschke–Minkowski homomorphisms. The Orlicz–Minkowski inequality for Orlicz mixed radial Blaschke–Minkowski homomorphisms is established. As an application, an Orlicz–Brunn–Minkowski inequality for the mixed radial Blaschke–Minkowski homomorphisms is also established, which in special case yields new $$L_p$$ L p Brunn–Minkowski inequality for mixed radial Blaschke–Minkowski homomorphisms.

中文翻译:

Orlicz 混合径向 Blaschke-Minkowski 同态

我们的主要目标是将混合径向 Blaschke-Minkowski 同态推广到 Orlicz 空间。通过计算混合径向 Blaschke-Minkowski 同态的调和 p -对偶 quermassintegrals 的一阶变化,我们引入了一个新的仿射几何量,并将其称为 Orlicz 混合径向 Blaschke-Minkowski 同态。建立 Orlicz 混合径向 Blaschke-Minkowski 同态的 Orlicz-Minkowski 不等式。作为应用,还建立了混合径向 Blaschke-Minkowski 同态的 Orlicz-Brunn-Minkowski 不等式,在特殊情况下,它会产生新的 $$L_p$$ L p Brunn-Minkowski 混合径向 Blaschke-Minkowski 同态不等式。
更新日期:2020-03-24
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