Small L2 curvature plus boundary second fundamental form close to the unit sphere forces a 3-manifold with boundary to be diffeomorphic to, and quantitatively close to, the Euclidean ball.
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Stability of the Euclidean 3-ball under L2-curvature pinching
Small L2 curvature plus boundary second fundamental form close to the unit sphere forces a 3-manifold with boundary to be diffeomorphic to, and quantitatively close to, the Euclidean ball.