Mean curvature in manifolds with Ricci curvature bounded from below
Mean curvature in manifolds with Ricci curvature bounded from below
Let M be a compact Riemannian manifold of nonnegative Ricci curvature and \Sigma a compact embedded 2-sided minimal hypersurface in M . It is proved that there is a dichotomy: If \Sigma does not separate M then \Sigma is totally geodesic and M\setminus\Sigma is isometric to the Riemannian product \Sigma\times(a,b) …