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＜E-Book＞
Curvature Measures of Singular Sets / by Jan Rataj, Martina Zähle
(Springer Monographs in Mathematics. ISSN:21969922)

Edition	1st ed. 2019.
Publisher	Cham : Springer International Publishing : Imprint: Springer
Year	2019
Size	XI, 256 p. 13 illus., 7 illus. in color : online resource
Authors	*Rataj, Jan author Zähle, Martina author SpringerLink (Online service)
Subjects	LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Measure theory LCSH:Convex geometry  LCSH:Discrete geometry LCSH:Geometry, Differential FREE:Global Analysis and Analysis on Manifolds FREE:Measure and Integration FREE:Convex and Discrete Geometry FREE:Differential Geometry
Notes	The book describes how curvature measures can be introduced for certain classes of sets with singularities in Euclidean spaces. Its focus lies on sets with positive reach and some extensions, which include the classical polyconvex sets and piecewise smooth submanifolds as special cases. The measures under consideration form a complete system of certain Euclidean invariants. Techniques of geometric measure theory, in particular, rectifiable currents are applied, and some important integral-geometric formulas are derived. Moreover, an approach to curvatures for a class of fractals is presented, which uses approximation by the rescaled curvature measures of small neighborhoods. The book collects results published during the last few decades in a nearly comprehensive way HTTP:URL=https://doi.org/10.1007/978-3-030-18183-3

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