Vorträge in der Woche 10.03.2014 bis 16.03.2014
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Donnerstag, 13.03.2014: Boundary regularity of Dirichlet minimizing Q-valued functions
Jonas Hirsch
F. Almgren considered a proof of a regularity result on area minimizing currents as the most pressing problem in geometric measure theory. His solution culminated in his pioneering work "Almgren's big regularity paper." In his opinion "central among his tools is utilization of Q-valued function to study branching phenomena." After a short introduction and motivation of Almgren's Q-valued functions we present a boundary regularity result. We have been able to extend the Hölder regularity for Dirichlet minimizing Q-valued functions up to the boundary. We assume C^1 regularity of the domain and C^{1,\alpha} regularity of the boundary data, \alpha> 1/2. After giving the precise statement and comparing it to the interior equivalent we will give an idea of our proof emphasising on similarities and differences to the interior situation. As time permits we conclude explaining why higher regularity results are difficult due to branching phenomena.
| Uhrzeit: | 14:15 |
| Ort: | N16 (M3) |
| Gruppe: | Oberseminar Geometrische Analysis und Mathematische Relativitätstheorie |
| Einladender: | Cederbaum, Huisken |
Donnerstag, 13.03.2014: A monotonicity formula for free boundary surfaces with respect to the unit ball
Alexander Volkmann (Albert Einstein Institut)
In the first part of this talk we will present a monotonicity identity for compact surfaces with free boundaries inside the boundary of the unit ball in $\mathbb R^n$ that have square integrable mean curvature. As one consequence we obtain a Li-Yau type inequality in this setting, thereby generalizing results of Oliveira and Soret, and Fraser and Schoen. In the second part of the talk we derive some sharp geometric inequalities for compact surfaces with free boundaries inside arbitrary orientable support surfaces. If time permits, we will present a sharp lower bound for the L1-tangent-point energy of closed curves in euclidean space thereby answering a question raised by Strzelecki, Szuma\'nska and von der Mosel.
| Uhrzeit: | 15:30 |
| Ort: | N16 (M3) |
| Gruppe: | Oberseminar Geometrische Analysis und Mathematische Relativitätstheorie |
| Einladender: | Cederbaum, Huisken |