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Second fundamental measure of geometric sets and local approximation of curvatures. (English) Zbl 1107.49029

Authors’ abstract: 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.

MSC:

49Q15 Geometric measure and integration theory, integral and normal currents in optimization
53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces
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