Minkowski valuations and generalized valuations

被引：25
|
作者：
Schuster, Franz E. [1 ]
Wannerer, Thomas [2 ]
机构：
[1] Vienna Univ Technol, Inst Discrete Math & Geometry, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria
[2] Friedrich Schiller Univ Jena, Inst Math, Ernst Abbe Pl 2, D-07743 Jena, Germany
来源：
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2018年 / 20卷 / 08期
基金：
欧洲研究理事会; 奥地利科学基金会;
关键词：
Minkowski valuations; generalized valuations; kinematic formula; Crofton formula; TRANSLATION-INVARIANT VALUATIONS; HARD LEFSCHETZ THEOREM; PROJECTION BODIES; CONVEX; TRANSFORMATIONS; CONVOLUTIONS;
D O I：
10.4171/JEMS/801
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A convolution representation of continuous translation-invariant and SO(n)-equivariant Minkowski valuations is established. This is based on a new classification of translation-invariant generalized spherical valuations. As applications, Crofton and kinematic formulas for Minkowski valuations are obtained.
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页码：1851 / 1884
页数：34
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