Limit leaves of an $H$ lamination are stable
William H. Meeks, Joaquín Pérez, Antonio R�os · Journal of Differential Geometry · 2010
Suppose $L$ is a lamination of a Riemannian manifold by hypersurfaces with the same constant mean curvature $H$. We prove that every limit leaf of $L$ is stable for the Jacobi operator. A simple but important consequence of this result is that the set of stable leaves of $L$ has the structure of a lamination.