×

zbMATH — the first resource for mathematics

Integral geometry of tame sets. (English) Zbl 1023.53057
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.

MSC:
53C65 Integral geometry
52A22 Random convex sets and integral geometry (aspects of convex geometry)
57N80 Stratifications in topological manifolds
PDF BibTeX XML Cite
Full Text: DOI