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Sphere Theorems for Immersed Hypersurfaces with Constant Scalar Curvature
We prove sphere theorems for closed connected immersed hypersurfaces of constant scalar curvature in Euclidean space. Combining Ros's rigidity argument with the filling theorem of Huisken and Sinestrari, we show that every two-convex such hypersurface is a round sphere. As a consequence, Yau's conje
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