Tuesday, October 29, 2024 - 10:15 in V3-204
Riesz energies and occupation measures
A talk in the Oberseminar Geometric Analysis series by
Michael Hinz from Bielefeld
| Abstract: |
If the mutual $\alpha$-Riesz energy of two Borel measures on $\mathbb{R}^n$ is finite, they cannot be too concentrated at the same spots. The finiteness of the $\alpha$-Riesz energy of a single Borel measure gives a lower bound on the Hausdorff dimension of its support. We apply these well-known principles to the occupation measures of H\"older continuous or (low) Sobolev regular mappings $u$. This gives new results on compositions with $BV$-functions with interesting consequences in stochastic analysis. If time permits, we will also describe current work in progress on related variational problems. The talk is based on joint work with Jonas T\"olle and Lauri Viitasaari (both Aalto University).
Within the CRC this talk is associated to the project(s): A3 |
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