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Curvature measures of singular sets

Rataj, Jan.

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Curvature measures of singular sets

Record Type:	Electronic resources : 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:

588970
Singularities (Mathematics)

LC Class. No.: QA614.58 / .R37 2019

Dewey Class. No.: 514.74

Curvature measures of singular sets
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100 1 $a Rataj, Jan. $3 3412524
245 1 0 $a Curvature measures of singular sets $h [electronic resource] / $c by Jan Rataj, Martina Zahle.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2019.
300 $a xi, 256 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer monographs in mathematics, $x 1439-7382
520 $a 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.
650 0 $a Singularities (Mathematics) $3 588970
650 0 $a Global analysis. $3 699669
650 0 $a Mathematics. $3 515831
650 0 $a Discrete groups. $3 661794
650 0 $a Global differential geometry. $3 705007
650 1 4 $a Global Analysis and Analysis on Manifolds. $3 891107
650 2 4 $a Measure and Integration. $3 891263
650 2 4 $a Convex and Discrete Geometry. $3 893686
650 2 4 $a Differential Geometry. $3 891003
700 1 $a Zahle, Martina. $3 2157947
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Springer monographs in mathematics. $3 1535313
856 4 0 $u https://doi.org/10.1007/978-3-030-18183-3
950 $a Mathematics and Statistics (Springer-11649)