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arXiv · 2204.04102

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

Michael Eichmair·Thomas Koerber·Jan Metzger·Felix Schulze
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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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Michael Eichmair, Thomas Koerber, Jan Metzger, Felix Schulze. 2022-04-08. Huisken-Yau-type uniqueness for area-constrained Willmore spheres. https://arxiv.org/abs/2204.04102

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