Lp Brunn-Minkowski型仿射均质积分不等式

经典的仿射均质积分不等式是Brunn-Minkowski理论中一个关键不等式.建立了L_p Brunn-Minkowski型仿射均质积分不等式,定义了L_p Brunn-Minkowski型仿射混合均质积分且推广得到了L_p Brunn-Minkowski型仿射混合均质积分不等式.     

L_p径向Blaschke-Minkowski同态的L_p对偶几何表面积

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L_p径向Blaschke-Minkowski同态.本文结合L_p对偶几何表面积,建立了L_p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L_p径向Blaschke-Minkowski同态的Busemann-Petty问题的肯定和否定形式.     

极小几何Lp积分曲率

本文给出了极小几何L_p(p≥1)积分曲率的定义.对于一个包含原点在其内部的凸体,主要证明了其L_p熵Petty体的存在性和唯一性.同时研究了极小几何L_p积分曲率和L_p熵Petty体的连续性.     

MAPS PRESERVING THE NORM OF THE POSITIVE SUM IN Lp SPACES

For 1

p）+be the set of positive elements in L_p with norm one.Assume that V₀:S(L_p（Ω₁）)₊→S(L_p（Ω₂）)₊ is a surjective norm-additive map;that is,‖V₀（x）+V₀（y）‖=‖x+y‖,?x,y∈S(L_p（Ω₁）)₊.In this paper,we show that V₀ can be extended to an isometry from L_p（Ω₁） onto L_p（Ω₂）.     

单子集映射mτ与标准部分逆映射st-1的同态性

在饱和模型中,讨论了单子集映射m_T及标准部分逆映射st^-1的同态性质.证明了m_T能扩张成一个σ-同态的充要条件是X是可数紧空间.在一定条件下,st^-1是Borelσ-代数上的σ-同态映射,当且仅当X是预Hausdorff的,并给出了一个正则测度的一个Loeb表示.     

p-Aleksandrov体的混合均值积分

探究了Brunn-Minkowski理论,引入了关于p-Aleksandrov体的混合均值积分,建立了相应的L_p Minkowski不等式和L_p Brunn-Minkowski不等式,当p=1,i=0时为HU与JIANG的结果.     

(p,q)-John椭球

本文主要研究(p,q)-John椭球.经典的John椭球和L_p John椭球均是(p,q)-John椭球的特殊情形.首先讨论(p,q)-John椭球的充分必要条件和连续性.得到了关于(p,q)-John椭球的不等式和包含关系,所得到的不等式和包含关系分别类似于Ball体积比不等式和John包含关系.     

Orlicz等周不等式

本文利用经典的Popoviciu不等式和Orlicz-Minkowski混合体积不等式,建立了凸体的广义Orlicz等周不等式.这个新的Orlicz等周不等式在特殊情况下,分别产生了经典的等周不等式,L_p-等周不等式和Orlicz等周不等式.     

半群ASn的秩

设A_n和Sing_n分别是X_n上的交错群和奇异变换半群.考虑变换半群AS_n=A_n∪Sing_n,证明了变换半群AS_n的秩为3.     

rK1∪Im的匹配等价图类

计算了rK₁∪I_m的匹配等价图的个数,并且刻画了rK₁∪I_m以及它的补图的匹配等价图类.     

Some inequalities for Lp radial Blaschke-Minkowski homomorphisms1

The notion of radial Blaschke-Minkowski homomorphisms was presented by Schuster. Afterwards, Wang et al. introduced L_p radial Blaschke-Minkowski homomorphisms. In this paper, associated with L_p-dual a?ne surface areas, we establish some inequalities including the Brunn-Minkowski type inequality, cyclic inequality and monotonic inequalities, and give an a?rmative answer and a negative answer of Busemann-Petty problem for the L_p radial Blaschke-Minkowski homomorphisms.     

On radial Blaschke-Minkowski homomorphisms

In this article we first establish a dual isoperimetric type inequality for mixed radial Blaschke-Minkowski homomorphisms of different orders. Second, we prove a dual Brunn-Minkowski-type and a dual Minkowski-type inequality for mixed radial Blaschke-Minkowski homomorphisms.     

Orlicz-Brunn-Minkowski inequality for radial Blaschke-Minkowski homomorphisms

Abstract

In this paper, we extend the Brunn-Minkowski inequality for radial Blaschke-Minkowski homomorphisms to an Orlicz setting and an Orlicz-Brunn-Minkowski inequality for radial Blaschke-Minkowski homomorphisms is established. The new Orlicz-Brun-Minkowski inequality in special case yields the L_p-Brunn-Minkowski inequality for the radial mixed Blaschke-Minkowski homomorphisms and the mixed intersection bodies, respectively.     

Some inequalities for radial Blaschke-Minkowski homomorphisms

We establish some Brunn-Minkowski type inequalities for radial Blaschke-Minkowski homomorphisms with respect to Orlicz radial sums and differences of dual quermassintegrals.     

多重星体的L_p-对偶混合几何表面积及其相关不等式

叶德平等人介绍了任意实数p(p≠-n)的多重凸体的L_p-混合几何表面积.本文给出了关于任意实数p(p≠n)的多重星体的L_p-对偶混合几何表面积的概念,并且建立了一些相关不等式.     

On Blaschke-Minkowski homomorphisms

In this article we establish a Brunn-Minkowski-type inequality for mixed Blaschke-Minkowski homomorphisms.     

Radial Blaschke–Minkowski homomorphisms and volume differences

In this paper we establish Minkowski, Brunn–Minkowski, and Aleksandrov-Fenchel type inequalities for volume differences of radial Blaschke–Minkowski homomorphisms.     

Convolutions and multiplier transformations of convex bodies

Rotation intertwining maps from the set of convex bodies in into itself that are continuous linear operators with respect to Minkowski and Blaschke addition are investigated. The main focus is on Blaschke-Minkowski homomorphisms. We show that such maps are represented by a spherical convolution operator. An application of this representation is a complete classification of all even Blaschke-Minkowski homomorphisms which shows that these maps behave in many respects similar to the well known projection body operator. Among further applications is the following result: If an even Blaschke-Minkowski homomorphism maps a convex body to a polytope, then it is a constant multiple of the projection body operator.

     

L p Brunn–Minkowski type inequalities for Blaschke–Minkowski homomorphisms

In this article, some Brunn–Minkowski type inequalities for (radial) Blaschke–Minkowski homomorphisms with respect to (radial) L _p Minkowski addition are established.