Curvature Measures of Singular Sets
Jan Rataj author Martina Zähle author
Format:Paperback
Publisher:Springer Nature Switzerland AG
Published:14th Aug '20
Currently unavailable, and unfortunately no date known when it will be back
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.
“The presentation is clear and concise, and detailed proofs are given. … The book is certainly well suited for the serious student or researcher in another field who wants to learn the topic. … Students will learn the rigorous theoretical foundations for the subject as well as meet a large number of interesting examples.” (Lars Olsen, Mathematical Reviews, April, 2021)
“The monograph is well-written and the main concepts are clearly explained and presented. The contents are a comprehensive collection of results published during the last decades. The material is accessible to graduate students with a good background in geometric measure theory, convex analysis, and differential geometry. For researchers the volume is attractive for its overall point-of-view and the broad presentation of the subject.” (Peter Massopust, zbMATH 1423.28001, 2019)
ISBN: 9783030181857
Dimensions: unknown
Weight: unknown
256 pages
1st ed. 2019