Lipschitz–Killing curvatures and polar images-Reference-Cited by-同舟云学术

Lipschitz–Killing curvatures and polar images

Published:2018-07-20 Issue:2 Volume:19 Page:205-230
ISSN:1615-7168
Container-title:Advances in Geometry
language:en
Short-container-title:

Author:

Dutertre Nicolas¹

Affiliation:

1. Laboratoire Angevin de Recherche en Mathématiques (LAREMA) , CNRS, Université ďAngers , F-49045 Angers , France

Abstract

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

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom-2018-0019/pdf

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