Minkowski Additive Operators Under Volume Constraints

被引：4
|
作者：
Abardia-Evequoz, Judit [1 ]
Colesanti, Andrea [2 ]
Saorin-Gomez, Eugenia [3 ]
机构：
[1] Goethe Univ Frankfurt Main, Inst Math, Robert Mayer Str 10, D-60054 Frankfurt, Germany
[2] Dipartimento Matemat U Dini, Viale Morgagni 67-A, I-50134 Florence, Italy
[3] Univ Magdeburg, Inst Algebra & Geometrie, Univ Pl 2, D-39106 Magdeburg, Germany
来源：
JOURNAL OF GEOMETRIC ANALYSIS | 2018年 / 28卷 / 03期
关键词：
Minkowski endomorphism; Rogers-Shephard inequality; Monotonicity; Difference body; SO(n)-equivariance; VALUATIONS; INVARIANT; TRANSFORMATIONS;
D O I：
10.1007/s12220-017-9909-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We investigate Minkowski additive, continuous, and translation invariant operators : Kn. Kn defined on the family of convex bodies such that the volume of the image (K) is bounded from above and below by multiples of the volume of the convex body K, uniformly in K. We obtain a representation result for an infinite subcone contained in the cone formed by this type of operators. Under the additional assumption of monotonicity or SO(n)- equivariance, we obtain new characterization results for the difference body operator.
引用
收藏
页码：2422 / 2455
页数：34
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