Minkowski content and local Minkowski content for a class of self-conformal sets

Uta Freiberg, Sabrina Kombrink

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

We investigate (local) Minkowski measurability of C 1+α images of self-similar sets. We show that (local) Minkowski measurability of a self-similar set K implies (local) Minkowski measurability of its image F and provide an explicit formula for the (local) Minkowski content of F in this case. A counterexample is presented which shows that the converse is not necessarily true. That is, F can be Minkowski measurable although K is not. However, we obtain that an average version of the (local) Minkowski content of both K and F always exists and also provide an explicit formula for the relation between the (local) average Minkowski contents of K and F.

Original languageEnglish
Pages (from-to)307-325
Number of pages19
JournalGeometriae Dedicata
Volume159
Issue number1
DOIs
Publication statusPublished - Aug 2012

Keywords

  • Conformal iterated function system
  • Fractal curvature measures
  • Minkowski content
  • Self-conformal set

ASJC Scopus subject areas

  • Geometry and Topology

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