Principal kinematic formulas for germs of closed definable sets

被引：1
|
作者：
Dutertre, Nicolas [1 ]
机构：
[1] Univ Angers, CNRS, LAREMA, SFR MATHSTIC, F-49000 Angers, France
来源：
ADVANCES IN MATHEMATICS | 2022年 / 399卷
关键词：
Kinematic formulas; Definable sets; Lipschitz-Killing curvatures; Polar invariants; REAL EQUISINGULARITY; CURVATURES; TOPOLOGY;
D O I：
10.1016/j.aim.2022.108251
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove two principal kinematic formulas for germs of closed definable sets in R-n, that generalize the Cauchy-Crofton formula for the density due to Comte and the infinitesimal linear kinematic formula due to the author. In this setting, we do not integrate on the space of euclidean motions SO(n) x R-n, but on the manifold SO(n) x Sn-1. (c) 2022 Elsevier Inc. All rights reserved.
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页数：54
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