Geometriae Dedicata

, Volume 159, Issue 1, pp 307–325 | Cite as

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

Original Paper

Abstract

We investigate (local) Minkowski measurability of \({\mathcal {C}^{1+\alpha}}\) 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.

Keywords

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

Mathematics Subject Classification (2010)

28A80 28A75 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Universität Siegen, FB 6—MathematikSiegenGermany
  2. 2.Universität Bremen, FB 3—MathematikBremenGermany

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