Joint Seminar

15.11.2018, 16:15  –  Free University of Berlin, Arnimallee 6, SR 025/026
Seminar "Topics in Geometric Analysis"

Cezar Oniciuc, Thomas Körber

16:15Cezar Oniciuc
Biharmonic immersions in spheres
We present unique continuation results for biharmonic maps and then we review classification results for biharmonic hypersurfaces in Euclidean spheres.
17:45Thomas Körber
Maximizers of the Hawking Mass in Asymptotically Flat Manifolds
The Hawking mass is a concept of quasi-local mass which can be used to measure the strength of the gravitational field in general relativity. To this end, it is an interesting problem to find area-prescribed surfaces which enclose a domain with a maximal amount of Hawking mass. In this talk, I will explain some new results which solve this problem in certain situations.By a result of Lamm, Metzger and Schulze, an exterior region of a small perturbation of the three dimensional Schwarzschild manifold can be foliated by area-prescribed critical points of the Hawking mass, so-called surfaces of Willmore type. It turns out that the leaves of this foliation maximize the Hawking mass outside of a compact region. In fact, they are the only surfaces of Willmore type with non-negative Hawking mass enclosing the compact set. The main ingredients in the proof of these facts are a careful application of the first variational formula for the area functional to estimate the barycenter of a sphere with non-negative Hawking mass as well as estimates of integral type to derive geometric properties of spheres of Willmore type. I will also discuss possible extensions of these results.
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