# Lipschitz-Killing curvatures and polar images

Abstract : We relate the Lipschitz-Killing measures of a definable set $X \subset \mathbb{R}^n$ in an o-minimal structure to the volumes of generic polar images. For smooth submanifolds of $\mathbb{R}^n$, such results were established by Langevin and Shifrin. Then we give infinitesimal versions of these results. As a corollary, we obtain a relation between the polar invariants of Comte and Merle and the densities of generic polar images.
Domain :

Cited literature [32 references]

https://hal.archives-ouvertes.fr/hal-01239927
Contributor : Nicolas Dutertre <>
Submitted on : Tuesday, December 8, 2015 - 2:31:13 PM
Last modification on : Monday, March 9, 2020 - 6:15:55 PM
Document(s) archivé(s) le : Wednesday, March 9, 2016 - 2:54:51 PM

### Files

CurvaturesPolar.pdf
Files produced by the author(s)

### Citation

Nicolas Dutertre. Lipschitz-Killing curvatures and polar images. Advances in Geometry, De Gruyter, 2019, 19 (2), pp.205-230. ⟨10.1515/advgeom-2018-0019⟩. ⟨hal-01239927⟩

Record views