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arXiv · 1706.09394

Constant mean curvature spheres in homogeneous three-manifolds

William H. Meeks·Pablo Mira·Joaquin Perez·Antonio Ros
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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.

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William H. Meeks, Pablo Mira, Joaquin Perez, Antonio Ros. 2017-06-28. Constant mean curvature spheres in homogeneous three-manifolds. https://arxiv.org/abs/1706.09394

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