A free boundary CMC surface in the 3-ball with traceless second fundamental form pinched by (2+H<x,N>)^2/2 is a spherical cap or a Delaunay annulus.
Cavalcante, Abra˜ ao Mendes, and Feliciano Vit´ orio, Vanishing theorems for the cohomology groups of free boundary submanifolds, Ann
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Gap phenomena for constant mean curvature surfaces
A free boundary CMC surface in the 3-ball with traceless second fundamental form pinched by (2+H<x,N>)^2/2 is a spherical cap or a Delaunay annulus.