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arXiv · 2107.06458

Free boundary constant mean curvature surfaces in a strictly convex three-manifold

Sung-Hong Min·Keomkyo Seo
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Abstract

Let $C$ be a strictly convex domain in a $3$-dimensional Riemannian manifold with sectional curvature bounded above by a constant and let $\Sigma$ be a constant mean curvature surface with free boundary in $C$. We provide a pinching condition on the length of the traceless second fundamental form on $\Sigma$ which guarantees that the surface is homeomorphic to either a disk or an annulus. Furthermore, under the same pinching condition, we prove that if $C$ is a geodesic ball of $3$-dimensional space forms, then $\Sigma$ is either a spherical cap or a Delaunay surface.

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Sung-Hong Min, Keomkyo Seo. 2021-07-14. Free boundary constant mean curvature surfaces in a strictly convex three-manifold. https://arxiv.org/abs/2107.06458

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