Abstract
Barbosa, do Carmo and Eschenburg proved in Barbosa and do Carmo (Math Z 185(3):339–353, 1984), Barbosa et al. (Math Z 197(1): 123–138, 1988) that the only stable compact hypersurfaces of constant mean curvature immersed in space forms are geodesic spheres. We give a more general result in a wide class of Riemannian manifold including space forms. The interest lies mostly on the simplicity of the proof.
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