Lp径向Blaschke-Minkowski同态的Lp对偶几何表面积  

Lp Dual Geominimal Surface Areas of Lp Radial Blaschke-Minkowski Homomorphisms

作　　者：赵霞 王卫东[1] Xia ZHAO;Wei Dong WANG(Department of Mathematics,College of Science,China Three Gorges University,Yichang 443002,P.R.China)

机构地区：[1]三峡大学理学院数学系,宜昌443002

出　　处：《数学学报（中文版）》2020年第4期409-416,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11371224);三峡大学硕士学位论文培优基金(2019SSPY144)。

摘　　要：2006年,Schuster提出了径向Blaschke-Minkowski同态的概念.随后,汪卫等人将其推广到Lp径向Blaschke-Minkowski同态.本文结合Lp对偶几何表面积,建立了Lp径向Blaschke-Minkowski同态的若干不等式,包括Brunn-Minkowski型不等式和单调不等式.并给出了Lp径向Blaschke-Minkowski同态的Busemann-Petty问题的肯定和否定形式.In 2006,Schuster introduced the concept of radial Blaschke-Minkowski homomorphisms.Afterwards,Wang et al.extended this notion to Lp radial Blaschke-Minkowski homomorphisms.In this paper,we establish some inequalities of Lp dual geominimal surface areas for Lp radial Blaschke-Minkowski homomorphisms,including the Brunn-Minkowski type and monotonic inequalities.And we give an affirmative form and a negative form of Busemann-Petty problem for Lp radial Blaschke-Minkowski homomorphisms.

关 键 词：Lp径向Blaschke-Minkowski同态 Lp对偶几何表面积 BRUNN-MINKOWSKI不等式 Busemann-Petty问题 

分 类 号：O184[理学—数学]