An extension of Jellett's theorem

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The aim of this work is to show that a star-shaped hypersurface of constant mean curvature into the Euclidean sphere S n + 1 must be a geodesic sphere. This result extends the one obtained by Jellett in 1853 for such type of surfaces in the Euclidean space R 3 . In order to do that we will compute a useful formula for the Laplacian of a new support function defined over a hypersurface M of a Riemannian manifold M ¯ .