Constant mean curvature hypersurfaces in noncompact symmetric spaces

Here, we compute the mean curvature of the geodesic sphere at any point in some symmetric spaces and determine the lower bound of the mean curvature of a closed hypersurface of constant mean curvature in it. With the Hessian Comparison Theorem, we also show that there is a lower bound for the mean curvature of any closed hypersurface of constant mean curvature in a manifold with a pole satisfying a curvature condition.