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Alexandrovs theorem asserts that spheres are the only closed embedded constant mean curvature hypersurfaces in space forms. In this paper, we consider Alexandrovs theorem in warped product manifolds and prove a rigidity result in the spirit of Alexandrovs theorem. Our approach generalizes the proofs of Reilly and Ros and, under more restrictive assumptions, it provides an alternative proof of a recent theorem of Brendle.
Alexandrovs soap bubble theorem asserts that spheres are the only connected closed embedded hypersurfaces in the Euclidean space with constant mean curvature. The theorem can be extended to space forms and it holds for more general functions of the p
In 1968, Simons introduced the concept of index for hypersurfaces immersed into the Euclidean sphere S^{n+1}. Intuitively, the index measures the number of independent directions in which a given hypersurface fails to minimize area. The earliest resu
In this paper we consider Serrins overdetermined problems in warped product manifolds and we prove Serrins type rigidity results by using the P-function approach introduced by Weinberger.
In this paper, based on the local comparison principle in [12], we study the local behavior of the difference of two spacelike graphs in a neighborhood of a second contact point. Then we apply it to the constant mean curvature equation in 3-dimension
We give a new proof of the generalized Minkowski identities relating the higher degree mean curvatures of orientable closed hypersurfaces immersed in a given constant sectional curvature manifold. Our methods rely on a fundamental differential system