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Curvature Measures of Singular Sets

Author: Jan Rataj; Martina Zähle
Publisher: Cham : Springer, 2019.
Series: Springer monographs in mathematics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Rataj, Jan.
Curvature Measures of Singular Sets.
Cham : Springer, ©2019
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jan Rataj; Martina Zähle
ISBN: 9783030181833 3030181839
OCLC Number: 1108533275
Description: 1 online resource (261 pages)
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.
Series Title: Springer monographs in mathematics.
Responsibility: Jan Rataj, Martina Zähle.

Abstract:

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  Read more...

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