Large area-constrained Willmore surfaces in asymptotically Schwarzschild 3-manifolds

23.11. bis 23.11.2021, 12:15_13:45  –  Room 2.09.2.22 Campus Golm, C9A03 Tübingen
Geometric Analysis, Differential Geometry and Relativity

Thomas Körber

In this talk, I will present recent work (joint with M. Eichmair) on large area-constrained Willmore surfaces in asymptotically Schwarzschild 3-manifolds. Using the method of Lyapunov-Schmidt reduction, we prove that the end of such a manifold is foliated by distinguished area-constrained Willmore spheres. The leaves are the unique area-constrained Willmore spheres with large area, non-negative Hawking mass, and distance to the center of the manifold at least a small multiple of the area radius. I will also discuss recent results on the geometric center of mass of this foliation.