AG Geometrische Analysis (Winter Semester 2017/18)
- Lecturer: Prof. Dr. Tobias Lamm
- Classes: Seminar (0125100)
- Weekly hours: 2
|Seminar:||Tuesday 14:00-15:30||SR 2.67|
|Thursday 11:30-13:00||SR 2.66|
|Lecturer||Prof. Dr. Tobias Lamm|
|Room 2.040 Kollegiengebäude Mathematik (20.30)|
- 09.45-11.15 (SR 1.067) Anna Siffert (Max-Planck-Institut für Mathematik, Bonn): Existence of metrics maximizing the first eigenvalue on closed surfaces
Abstract: We prove that for closed surfaces of fixed topological type, orientable or non-orientable, there exists a unit volume metric, smooth away from finitely many conical singularities, that maximizes the first eigenvalue of the Laplace operator among all unit volume metrics. The key ingredient are several monotonicity results, which have partially been conjectured to hold before. This is joint work with Henrik Matthiesen.
- 14.00-15.30 (SR 2.067) Ana Karla Garcia Perez (KIT): Sphere bundles with 1/4-pinched fiberwise metrics
Abstract: This talk is going to be about the paper of Thomas Farrell, Zhou Gang, Dan Knopf, and Pedro Ontaneda, "Sphere bundles with 1/4-pinched fiberwise metrics". In the paper, they proved that there aren't many sphere bundles which support strictly 1/4-pinched curved Riemannian metrics on their fibers. We are going to focus on the techniques they used in order to have some control of the Ricci flow, which is one of the main tools to prove the result of the paper.
- 11.30-12.30 (SR 2.066) Huy Nguyen (Queen Mary University of London): Mean curvature flow with Quadratic Curvature Bounds
Abstract: In this talk we will discuss mean curvature flow with quadratic curvature bounds. We firstly will discuss improvements to the Andrews-Baker result for higher co-dimension for surfaces of co-dimension two. We will then classify ancient solutions to high codimension mean curvature flow under a natural pinching condition and finally we will discuss singularity formation of the mean curvature flow in the sphere without positive mean curvature.
- 14.00-15.00 (SR 2.067) Ben Sharp (University of Warwick): Minimal hypersurfaces in Riemannian manifolds
Abstract: Minimal hypersurfaces are critical points of the volume functional, and the Morse index tells us how many ways one can decrease their volume locally. We will present an overview of recent results which relate the Morse index to the geometry and topology of minimal hypersurfaces. These are joint works with Lucas Ambrozio-Alessandro Carlotto and Reto Buzano.