U petak, 14.03.2025., u 16 h u dvorani 104,

Steffen Winter, Karlsruhe University, održat će seminar pod naslovom:

On support measures, Minkowski content and complex dimensions.

 

*Abstract:* For any given closed set inR^d, the general Steiner formula
of Hug, Last and Weil describes its tube volume and the support measures
arising from this formula encode its geometric properties. However, it
is not easy to extract fractal properties of a set directly from these
measures. We introduce some new geometric functionals for compact
subsets of R^d which we call basic functionals and support functionals,
which are tightly related to the support measures. We connect
appropriate scaling exponents of these functionals to the (upper)
Minkowski dimension of the set and explain how its Minkowski content may
be represented in terms of these functionals. Our original motivation
was to elucidate the geometric meaning of the coefficients in fractal
tube formulas that arise in the theory of complex dimensions by Lapidus,
Zubrinic and Radunovic. We explain the relations and also comment on the
connections to fractal curvatures. Based on joint work with Goran
Radunovic.

 

Pozivaju se svi zainteresirani.

 

Maja Resman