Tuesday, January 7, 2020 - 10:15 in V4-112
Removable sets and uniqueness of operator extensions on manifolds and metric measure spaces
A talk in the Oberseminar Geometric Analysis series by
Michael Hinz from Bielefeld
| Abstract: |
We study removable sets (in the sense of Mazja) and $L^p$-uniqueness problems on manifolds and metric measure spaces. The Laplacian, considered on suitable spaces of test functions vanishing in a neighborhood of a 'removed' null set, has a unique extension if and only if this set has vanishing second order capacity. If the semigroup is strong Feller and satisfies a specific gradient inequality then two types of capacities are comparable and the critical size of the removed set can be expressed in terms of Hausdorff measures. As an application we show that from the point of view of essential self-adjointness the Laplacian on certain Gromov-Hausdorff limits of non-collapsing spaces 'ignores' the singular part of the limit space. This is joint work with Jun Masamune (Sapporo) and Kohei Suzuki (Pisa).
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