Lipschitz–Killing curvatures and polar images

Nicolas Dutertre 1
  • 1 Laboratoire Angevin de Recherche en Mathématiques (LAREMA), CNRS, Université ďAngers, F-49045, Angers, France
Nicolas Dutertre
  • Corresponding author
  • Laboratoire Angevin de Recherche en Mathématiques (LAREMA), CNRS, Université ďAngers, F-49045, Angers, France
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Abstract

We relate the Lipschitz–Killing measures of a definable set X ⊂ ℝn in an o-minimal structure to the volumes of generic polar images. For smooth submanifolds of ℝn, 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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