Speaker:Tomas Persson (Lund)
Title:
Potentials, energies and Hausdorff dimension
Abstract:
The Hausdorff dimension of a set is a number, not necessarily an integer,
which measures the fractal dimension of the set.
There is a classical connection between Riesz-potentials, Riesz-energies
and Hausdorff dimension. Otto Frostman (Lund) proved in his 1935 thesis that
if E is a set and \mu is a measure with support in E, then the Hausdorff dimension
of E is at least s if the s-dimensional Riesz-energy of \mu is finite.
I will first define the above mentioned concepts and then give Frostman's result
and some of its applications.
Later in the talk, I will mention some new methods where Hausdorff dimension is
calculated using potentials and energies with inhomogeneous kernels.
Some applications are in stochastic geometry and dynamical systems.