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

초록

Let C be a strictly convex domain in a three-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 three-dimensional space forms, then Sigma is either a spherical cap or a Delaunay surface.

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