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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.
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https://hal.archives-ouvertes.fr/hal-01239927
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Submitted on : Tuesday, December 8, 2015 - 2:31:13 PM
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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⟩

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