Bibliograph

Curvature Measures of Singular Sets, by Jan Rataj, Martina Zähle

Type

Label

Curvature Measures of Singular Sets, by Jan Rataj, Martina Zähle

Language

eng

resource.imageBitDepth

Literary Form

non fiction

Main title

Curvature Measures of Singular Sets

Medium

electronic resource

Nature of contents

dictionaries

Oclc number

1108533275

Responsibility statement

by Jan Rataj, Martina Zähle

Series statement

Springer Monographs in Mathematics,, 1439-7382Springer eBooksSpringer eBooks.

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 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.--, Provided by publisher

Contributor