AG Geometrische Analysis (Summer Semester 2017)
- Lecturer: Prof. Dr. Tobias Lamm
- Classes: Seminar (0176600)
- Weekly hours: 2
|Seminar:||Tuesday 14:00-15:30||SR 2.67|
|Thursday 11:30-13:00||SR 3.61|
|Lecturer||Prof. Dr. Tobias Lamm|
|Room 2.040 Kollegiengebäude Mathematik (20.30)|
- May 2nd 2017 (Tuesday), 2 p.m. (SR 2.067): Alix Deruelle (Université Pierre et Marie Curie)
Title: Expanders of the harmonic map flow
Abstract: Expanding self-similarities of a given evolution equation create an ambiguity in the
continuation of the flow after it reached a first singularity. In this talk, we investigate the
possibility of smoothing out any map from the n-sphere, , to another sphere, that is homotopic
to a constant by a self-similarity of the harmonic map flow. To do so, in the spirit of Chen-Struwe,
we introduce a one-parameter family of Ginzburg-Landau equations that exhibit the same homogeneity
and once the existence of expanders for this family is granted, we pass to the limit. We also study
the singular set of such solutions as well as the uniqueness issue.
The talk is based on joint work with Tobias Lamm.
- June 13th 2017 (Tuesday), 1 p.m. (SR 2.067): Paola Pozzi (Universität Duisburg-Essen)
Title: On the elastic flow of open curves in
Abstract: In this talk I will discuss the evolution of regular open curves in moving according to the -gradient flow of the elastic energy and subject to different sets of boundary conditions and constraints on the length of the curve.
The results presented are based on joint works with Anna Dall’Acqua and Chun-Chi Lin.
- June 16th 2017 (Friday), 11.30 a.m. (SR 2.067): Ernst Kuwert (Universität Freiburg)
Title: Willmore minimizers with prescribed isoperimetric ratio
Abstract: We discuss the existence of surfaces of type minimizing the Willmore functional with prescribed isoperimetric ratio, and some asymptotics as the ratio goes to zero.
- June 22nd 2017 (Thursday), 11.30 a.m. (SR 3.061): Jan Metzger (Universität Potsdam)
Title: On the uniqueness of small surfaces minimizing the Willmore functional subject to a small area constraint
Abstract: We consider the Willmore functional for surfaces immersed in a compact Riemannian manifold M and study minimizers subject to a small area constratint. We show that if the scalar curvature of M has a non-degenerate maximum then for small enough area these minimizers are unique. This is joint work with Tobias Lamm and Felix Schulze.
- June 27th 2017 (Tuesday), 2 p.m. (SR 2.067): Reto Buzano (Queen Mary University of London)
Title: The moduli space of two-convex embedded spheres and tori
Abstract: It is interesting to study the topology of the space of smoothly embedded n-spheres in . By Smale’s theorem, this space is contractible for and by Hatcher’s proof of the Smale conjecture, it is also contractible for . These results are of great importance, generalising in particular the Schoenflies theorem and Cerf’s theorem. In this talk, I will explain how mean curvature flow with surgery can be used to study a higher-dimensional variant of these results, proving in particular that the space of two-convex embedded spheres is path-connected in every dimension n. We then also look at the space of two-convex embedded tori where the question is more intriguing and the result in particular depends on the dimension n. This is all joint work with Robert Haslhofer and Or Hershkovits.