Second fundamental measure of geometric sets and local approximation of curvatures

David Cohen-Steiner, Jean-Marie Morvan

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)363-394
Number of pages32
JournalJournal of Differential Geometry
Volume74
Issue number3
DOIs
StatePublished - Jan 1 2006

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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