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

作者：Freiberg Uta; Kombrink Sabrina^*

来源：Geometriae Dedicata, 2012, 159(1): 307-325.

DOI：10.1007/s10711-011-9661-5

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

We investigate (local) Minkowski measurability of 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.

• 出版日期2012-8