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Advances in Geometry

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Lipschitz–Killing curvatures and polar images

Nicolas Dutertre
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  • Laboratoire Angevin de Recherche en Mathématiques (LAREMA), CNRS, Université ďAngers, F-49045 Angers, France
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Published Online: 2018-07-20 | DOI: https://doi.org/10.1515/advgeom-2018-0019

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.

Keywords: Lipschitz–Killing curvatures; stratified Morse theory; polar varieties; polar images; o-minimal sets; generic projections; fold points

MSC 2010: 14B05; 53C65; 58K05

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About the article


Received: 2017-01-12

Revised: 2017-04-25

Published Online: 2018-07-20


Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2018-0019.

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