03243nam 22006375 450 991033824540332120240123100523.03-030-18183-910.1007/978-3-030-18183-3(CKB)4100000008493346(DE-He213)978-3-030-18183-3(MiAaPQ)EBC5797247(PPN)258059133(EXLCZ)99410000000849334620190622d2019 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierCurvature Measures of Singular Sets /by Jan Rataj, Martina Zähle1st ed. 2019.Cham :Springer International Publishing :Imprint: Springer,2019.1 online resource (XI, 256 p. 13 illus., 7 illus. in color.)Springer Monographs in Mathematics,1439-73823-030-18182-0 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.Springer Monographs in Mathematics,1439-7382Global analysis (Mathematics)Manifolds (Mathematics)Measure theoryConvex geometry Discrete geometryDifferential geometryGlobal Analysis and Analysis on Manifoldshttps://scigraph.springernature.com/ontologies/product-market-codes/M12082Measure and Integrationhttps://scigraph.springernature.com/ontologies/product-market-codes/M12120Convex and Discrete Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21014Differential Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21022Global analysis (Mathematics).Manifolds (Mathematics).Measure theory.Convex geometry .Discrete geometry.Differential geometry.Global Analysis and Analysis on Manifolds.Measure and Integration.Convex and Discrete Geometry.Differential Geometry.514.74514.74Rataj Jan1962-authttp://id.loc.gov/vocabulary/relators/aut1494525Zähle Martinaauthttp://id.loc.gov/vocabulary/relators/autBOOK9910338245403321Curvature Measures of Singular Sets3718093UNINA