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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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Volume 19, Issue 2


Lipschitz–Killing curvatures and polar images

Nicolas Dutertre
  • Corresponding author
  • 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


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

Published in Print: 2019-04-24

Communicated by: T. Grundhöfer

Citation Information: Advances in Geometry, Volume 19, Issue 2, Pages 205–230, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2018-0019.

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