16:15 Uhr | Emanuele Spadaro | Semicontinuous energies for multiple valued functions
In the late '70s, motivated by the study of higher codimension
minimal surfaces, F. Almgren introduced the notion of multiple valued
functions minimizing the Dirichlet energy. As pointed out later by P.
Mattila, Almgren's approach does not extend to the case of elliptic
quadratic energies. In this talk I will present a complete
characterization of lower semicontinuous functionals defined on Sobolev
spaces of multiple valued functions, recovering earlier results by P.
Mattila as special case and answering to one of his conjectures. This is
a joint work with M. Focardi (Firenze) and C. De Lellis (Zuerich).
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17:45 Uhr | Felix Jachan | Aspects of area preserving Willmore Flow
We consider hypersurfaces in 3-manifolds moving by an area
preserving variant of the Willmore Flow, focusing on 'large'
spheres in asymptotically Schwarzschild ambient metrics.
We study short time existence and, largely relying on
techniques used by Kuwert & Schätzle in the early '00s for
Willmore flow in Euclidean Space, give generalizations of
their observations concerning the minimal existence time and
Blow-up-behaviour around singularities, adressing issues
arising from the ambient curvature and from non-local terms
in our flow equation. This is work in progress and, as part
of an ongoing PhD thesis, contains a couple of rough edges. |