Huisken-Yau-type uniqueness for area-constrained Willmore spheres

02.06. bis 02.06.2022, 14:00-15:30  –  C6H05 Tübingen, 2.09.2.22 Campus Golm
Geometric Analysis, Differential Geometry and Relativity

Jan Metzger

Let (M, g) be a Riemannian 3-manifold that is asymptotic to Schwarzschild. We study large area-constrained Willmore spheres $\Sigma\subset M$ with non-negative Hawking mass and inner radius $\rho$ dominated by the area radius $\lambda$.
We show that if the scalar curvature of $(M,g)$ is non-negative,
then there are no such surfaces with $\log\lambda \ll \rho$.