Potentials, energies and Hausdorff dimension

Tomas Persson
Lund University, Sweden

Date(s) : 31/10/2017   iCal
11 h 00 min - 12 h 00 min

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 talk about Frostman’s result and some of its applications. I will then mention some new methods were Hausdorff dimension is calculated using potentials and energies with inhomogeneous kernels. Some applications are in stochastic geometry and dynamical systems.




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