Constant mean curvature spheres in homogeneous three-manifolds

Abstract

We prove that two spheres of the same constant mean curvature in an arbitrary homogeneous three-manifold only differ by an ambient isometry, and we determine the values of the mean curvature for which such spheres exist. This gives a complete classification of immersed constant mean curvature spheres in three-dimensional homogeneous manifolds.

80 pages, 8 figures. This works contains an Appendix (Section 9) that previously appeared within arXiv:1606.08015