Sabrina Kombrink: Steiner formula for fractal sets

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.