Title: The diameter of an immersed Riemannian manifold with bounded mean curvature
Abstract: Abstract Let M be an n -dimensional complete Riemannian manifold with Ricci curvature bounded from below. Let be an N -dimensional ( N < n ) complete, simply connected Riemannian manifold with nonpositive sectional curvature. We shall prove in this note that if there exists an isometric immersion φ of M into with the property that the immersed manifold is contained in a ball of radius R and that the mean curvature vector H of the immersion has bounded norm ∥ H ∥ > H 0 , ( H 0 > 0) then R > H −1 0 .