Integral Geometry of Tame Sets
- Cite this article as:
- Bröcker, L. & Kuppe, M. Geometriae Dedicata (2000) 82: 285. doi:10.1023/A:1005248711077
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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.