Curvature Measures Of Singular Sets by Jan RatajCurvature Measures Of Singular Sets by Jan Rataj

Curvature Measures Of Singular Sets

byJan Rataj, Martina Zähle

Hardcover | July 13, 2019

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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.
Jan Rataj, born in 1962 in Prague, studied at Charles University in Prague and defended his PhD at the Mathematical Institute of the Czech Academy of Sciences in 1991. He has been affiliated to Charles University in Prague since 1992, as full professor since 2000. He is the author of approximately 55 publications (on probability theory...
Title:Curvature Measures Of Singular SetsFormat:HardcoverProduct dimensions:220 pages, 9.41 × 7.24 × 0.98 inShipping dimensions:9.41 × 7.24 × 0.98 inPublished:July 13, 2019Publisher:Springer NatureLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3030181820

ISBN - 13:9783030181826


Table of Contents

- Background from Geometric Measure Theory. - Background from Convex Geometry. - Background from Differential Geometry and Topology. - Sets with Positive Reach. - Unions of Sets with Positive Reach. - Integral Geometric Formulae. - Approximation of Curvatures. - Characterization Theorems. - Extensions of Curvature Measures to Larger set Classes. - Fractal Versions of Curvatures.