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

Autoren: Michael Eichmair, Thomas Koerber, Jan Metzger, Felix Schulze (2022)

Let (M,g) be a Riemannian 3-manifold that is asymptotic to Schwarzschild. We study the existence of large area-constrained Willmore spheres $$\Sigma\subset M$$ with non-negative Hawking mass and inner radius $$\rho$$ dominated by the area radius $$\lambda$$. If the scalar curvature of $$(M,g)$$ is non-negative, we  show that no such surfaces with $$\log \lambda \ll \rho$$ exist. This answers a question of G. Huisken.

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