Tomas Persson: Potentials, energies and Hausdorff dimension
Tid: Ti 2017-11-14 kl 14.00
Föreläsare: Tomas Persson, Lund University
Plats: Institut Mittag-Leffler, Auravägen 17, Djursholm
There is a classical connection between Riesz-potentials, Riesz-energies and Hausdorff dimension. Otto Frostman (Lund) proved in his thesis that if E is a set and μ is a measure with support in E, then the Hausdorff dimension of E is at least s if the s-dimensional Riesz-energy of μ is finite.
I will first recall Frostman's result and some of its applications. I will then 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.