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.
"Limit leaves of an $H$ lamination are stable." J. Differential Geom. 84 (1) 179 - 189, January 2010. https://doi.org/10.4310/jdg/1271271797