Upper semicontinuous valuations on the space of convex discs

被引：5

作者：

Ludwig, M ^{[1
]}

机构：

[1] Vienna Tech Univ, Abt Anal, A-1040 Vienna, Austria

来源：

GEOMETRIAE DEDICATA | 2000年 / 80卷 / 1-3期

关键词：

convex disc; valuation; Hadwiger's characterization theorem; curvature integral;

D O I：

10.1023/A:1005240024644

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that every rigid motion invariant and upper semicontinuous valuation on the space of convex discs is a linear combination of the Euler characteristic, the length, the area, and a suitable curvature integral of the convex disc.

引用

页码：263 / 279

页数：17

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