IUMJ

Title: Compact stable constant mean curvature surfaces in homogeneous 3-manifolds

Authors: Francisco Torralbo and Francisco Urbano

Issue: Volume 61 (2012), Issue 3, 1129-1156

Abstract:

We classify the stable constant mean curvature spheres in the homogeneous Riemannian $3$-manifolds: the Berger spheres, the special linear group, and the Heisenberg group. We show that all of them are stable in the last two cases, while in some Berger spheres there are unstable ones. Also, we classify the stable compact orientable constant mean curvature surfaces in a certain subfamily of the Berger spheres. This allows us to solve the isoperimetric problem in some Berger spheres.