Book Details
Format
Paperback / Softback
Book Series
Springer Monographs in Mathematics
ISBN-10
3030181855
ISBN-13
9783030181857
Edition
2019 ed.
Publisher
Springer Nature Switzerland AG
Imprint
Springer Nature Switzerland AG
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Aug 14th, 2020
Print length
256 Pages
Product Classification:
Euclidean geometry
Ksh 19,800.00
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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 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.
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