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.

引用

页码：1851 / 1884

页数：34

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