Open Access
November 2006 Second fundamental measure of geometric sets and local approximation of curvatures
David Cohen-Steiner, Jean-Marie Morvan
J. Differential Geom. 74(3): 363-394 (November 2006). DOI: 10.4310/jdg/1175266231


Using the theory of normal cycles, we associate with each geometric subset of a Riemannian manifold a —tensor-valued— curvature measure, which we call its second fundamental measure. This measure provides a finer description of the geometry of singular sets than the standard curvature measures. Moreover, we deal with approximation of curvature measures. We get a local quantitative estimate of the difference between curvature measures of two geometric subsets, when one of them is a smooth hypersurface.


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David Cohen-Steiner. Jean-Marie Morvan. "Second fundamental measure of geometric sets and local approximation of curvatures." J. Differential Geom. 74 (3) 363 - 394, November 2006.


Published: November 2006
First available in Project Euclid: 30 March 2007

zbMATH: 1107.49029
MathSciNet: MR2269782
Digital Object Identifier: 10.4310/jdg/1175266231

Primary: 53Cxx
Secondary: 49Q20

Rights: Copyright © 2006 Lehigh University

Vol.74 • No. 3 • November 2006
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