Limit leaves of a CMC lamination are stable

Abstract

Suppose $\mathcal{L}$ is a lamination of a Riemannian manifold by hypersurfaces with the same constant mean curvature. We prove that every limit leaf of $\mathcal{L}$ is stable for the Jacobi operator. A simple but important consequence of this result is that the set of stable leaves of $\mathcal{L}$ has the structure of a lamination.

10 pages, 3 figures, replacement: minor changes in the introduction + notation

Cited by in corpus (1)

• On the moduli of constant mean curvature cylinders of finite type in the 3-sphere