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Lipschitz–Killing curvatures and polar images

Nicolas Dutertre
From the journal Advances in Geometry

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.

MSC 2010: 14B05; 53C65; 58K05

  1. Communicated by: T. Grundhöfer

Acknowledgements

The author thanks David Mond and Terry Gaffney for interesting discussions on double points of fold singularities.

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Received: 2017-01-12
Revised: 2017-04-25
Published Online: 2018-07-20
Published in Print: 2019-04-24

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