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The Steiner formula for sets with irregular boundary - and what information on the sound of a drum with irregular boundary it can reveal
15.11.2018, 16:15 - 17:15
Speaker:Prof. Dr. Sabrina Kombrink, Georg-August-Universität Göttingen
Location:Mathematisches Institut, Bunsenstr 3-5SitzungszimmerGras Geo Map
Organizer:Mathematisches Institut
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 irregular 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 and spectral information which the analogues of the exponents and coefficients incorporate, linking in to the question which geometric information one can gain from listening to the sound of a drum with irregular boundary.
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Host:Prof. Dr. Dorothea Bahns
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