Large outlying stable constant mean curvature spheres in initial data sets

• 成果类型: Article
• 署名作者: Brendle, Simon; Eichmair, Michael
• 署名单位: Stanford University; Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-013-0494-8
• 发表日期: 2014
• 页码: 663-682
• 关键词: surfaces; foliations

摘要

We give examples of asymptotically flat three-manifolds which admit arbitrarily large constant mean curvature spheres that are far away from the center of the manifold. This resolves a question raised by Huisken and Yau (Invent Math 124:281-311, 1996). On the other hand, we show that such surfaces cannot exist when has nonnegative scalar curvature. This result depends on an intricate relationship between the scalar curvature of the initial data set and the isoperimetric ratio of large stable constant mean curvature surfaces.