Steiner formula for fractal sets

Fractal Geometry and Dynamics

14 September 14:00 - 14:50

Sabrina Kombrink - University of Birmingham

The famous Steiner formula for a non-empty compact convex subset $K$ of the $d$-dimensional Euclidean space states that the volume of the $\epsilon$-parallel set of $K$ can be expressed as a polynomial in $\epsilon$ of degree $d$. The coefficients of the polynomial carry important information on the geometry of the convex set, such as the volume, the surface area and the Euler characteristic. For fractal sets the $\epsilon$-parallel volume is more involved and cannot be written as an ordinary polynomial in $\epsilon$. In this talk we discuss the behaviour of the $\epsilon$-parallel volumes of certain fractals and analogues of the Steiner formula. Moreover we explore the geometric information which the analogues of the exponents and coefficients incorporate.
Kenneth Falconer
University of St Andrews
Maarit Järvenpää
University of Oulu
Antti Kupiainen
University of Helsinki
Francois Ledrappier
University of Notre Dame
Pertti Mattila
University of Helsinki


Maarit Järvenpää


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