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Curvature measures of singular sets

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Curvature measures of singular sets

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Curvature measures of singular sets/ by Jan Rataj, Martina Zahle.
作者:	Rataj, Jan.
其他作者:	Zahle, Martina.
出版者:	Cham :Springer International Publishing : : 2019.,
面頁冊數:	xi, 256 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Singularities (Mathematics) -
電子資源:	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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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.
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