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

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arxiv 2204.04102 v2 pith:Y4AEEAYF submitted 2022-04-08 math.DG

Michael Eichmair , Thomas Koerber , Jan Metzger , Felix Schulze This is my paper · ORCID
classification math.DG
keywords area-constrainedlambdanon-negativeradiussphereswillmoreanswersarea
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abstract

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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