## Journal of Differential Geometry

### Limit leaves of an $H$ lamination are stable

#### Abstract

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.

#### Article information

Source
J. Differential Geom., Volume 84, Number 1 (2010), 179-189.

Dates
First available in Project Euclid: 14 April 2010

https://projecteuclid.org/euclid.jdg/1271271797

Digital Object Identifier
doi:10.4310/jdg/1271271797

Mathematical Reviews number (MathSciNet)
MR2629513

Zentralblatt MATH identifier
1197.53037

#### Citation

Meeks, William H.; Pérez, Joaquín; Ros, Antonio. Limit leaves of an $H$ lamination are stable. J. Differential Geom. 84 (2010), no. 1, 179--189. doi:10.4310/jdg/1271271797. https://projecteuclid.org/euclid.jdg/1271271797