Constant mean curvature spheres in homogeneous three-manifolds
Differential Geometry
2017-06-29 v1 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.1706.09394,
title = {Constant mean curvature spheres in homogeneous three-manifolds},
author = {William H. Meeks and Pablo Mira and Joaquin Perez and Antonio Ros},
journal= {arXiv preprint arXiv:1706.09394},
year = {2017}
}
Comments
80 pages, 8 figures. This works contains an Appendix (Section 9) that previously appeared within arXiv:1606.08015