عنوان

Curvature Measures of Singular Sets /

3030181839

9783030181833

3030181820

9783030181826

Curvature Measures of Singular Sets /

[Book]

Jan Rataj, Martina Zähle.

Cham :

Springer,

2019.

1 online resource (261 pages)

Springer Monographs in Mathematics Ser.

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.--

Curvature Measures of Singular Sets.

9783030181826

Discrete groups.

Global analysis.

Global differential geometry.

Mathematics.

Singularities (Mathematics)

Discrete groups.

Global differential geometry.

Mathematics.

Singularities (Mathematics)

Rataj, Jan,1962-

Zähle, Martina,1950-

20200823090114.0

pn

[Book]

Y