Integral geometry of tame sets

被引：44

作者：

Bröcker, L ^{[1
]}

Kuppe, M ^{[1
]}

机构：

[1] Univ Munster, Inst Math, D-48149 Munster, Germany

来源：

GEOMETRIAE DEDICATA | 2000年 / 82卷 / 1-3期

关键词：

integral geometry; tame stratifications;

D O I：

10.1023/A:1005248711077

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Curvature measures on certain tame Whitney-stratified sets are defined as coefficients of modified volume-growth polynomials. Stratified Morse theory yields alternative descriptions of these curvature measures for tame (possibly highly singular) sets. From this we obtain a generalized Gauss-Bonnet formula and various kinematic formulas. Finally, for O-minimal sets it is shown that curvature measures only depend on the inner metric.

引用

页码：285 / 323

页数：39

共 32 条

[1] The Gauss-Bonnet theorem for Riemannian polyhedra [J].