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Curvature measures of singular sets
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SpringerLink (Online service)
Curvature measures of singular sets
Record Type:
Language materials, printed : Monograph/item
Title/Author:
Curvature measures of singular sets/ by Jan Rataj, Martina Zahle.
Author:
Rataj, Jan.
other author:
Zahle, Martina.
Published:
Cham :Springer International Publishing : : 2019.,
Description:
xi, 256 p. :ill., digital ; : 24 cm.;
Contained By:
Springer eBooks
Subject:
Singularities (Mathematics) -
Online resource:
https://doi.org/10.1007/978-3-030-18183-3
ISBN:
9783030181833
Curvature measures of singular sets
Rataj, Jan.
Curvature measures of singular sets
[electronic resource] /by Jan Rataj, Martina Zahle. - Cham :Springer International Publishing :2019. - xi, 256 p. :ill., digital ;24 cm. - Springer monographs in mathematics,1439-7382. - Springer monographs in mathematics..
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.
ISBN: 9783030181833
Standard No.: 10.1007/978-3-030-18183-3doiSubjects--Topical Terms:
527840
Singularities (Mathematics)
LC Class. No.: QA614.58 / .R37 2019
Dewey Class. No.: 514.74
Curvature measures of singular sets
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by Jan Rataj, Martina Zahle.
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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.
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Mathematics and Statistics (Springer-11649)
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