Constant mean curvature spheres in homogeneous three-manifolds

• 成果类型: Article
• 署名作者: Meeks, William H., III; Mira, Pablo; Perez, Joaquin; Ros, Antonio
• 署名单位: University of Massachusetts System; University of Massachusetts Amherst; Universidad Politecnica de Cartagena; University of Granada; University of Granada
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-020-01008-y
• 发表日期: 2021
• 页码: 147-244
• 关键词: s-2 x r; isoperimetric domains; minimal-surfaces; MANIFOLDS; EXISTENCE; TOPOLOGY

摘要

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.