Compact stable constant mean curvature surfaces in the Berger spheres
Differential Geometry
2009-06-09 v1
Abstract
In the 1-parameter family of Berger spheres S^3(a), a > 0 (S^3(1) is the round 3-sphere of radius 1) we classify the stable constant mean curvature spheres, showing that in some Berger spheres (a close to 0) there are unstable constant mean curvature spheres. Also, we classify the orientable compact stable constant mean curvature surfaces in S^3(a), 1/3 <= a < 1 proving that they are spheres or the minimal Clifford torus in S^3(1/3). This allows to solve the isoperimetric problem in these Berger spheres.
Keywords
Cite
@article{arxiv.0906.1439,
title = {Compact stable constant mean curvature surfaces in the Berger spheres},
author = {Francisco Torralbo and Francisco Urbano},
journal= {arXiv preprint arXiv:0906.1439},
year = {2009}
}
Comments
21 pages, 7 figures