Compact stable constant mean curvature surfaces in the Berger spheres

Details Compact stable constant mean curvature surfaces in the Berger spheres Compact stable constant mean curvature surfaces in the Berger spheres

2009-06-08

arxiv.org/abs/0906.1439v1

Mathematics

Differential Geometry

21 pages, 7 figures

Scientific paper

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.

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