Limit lamination theorem for H-disks

• 成果类型: Article
• 署名作者: Meeks, William H., III; Tinaglia, Giuseppe
• 署名单位: University of Massachusetts System; University of Massachusetts Amherst; University of London; King's College London
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-021-01049-x
• 发表日期: 2021
• 页码: 393-420
• 关键词: embedded minimal-surfaces; constant mean-curvature; fixed genus; SPACE

摘要

We describe the lamination limits of sequences of compact disks M-n embedded in R-3 with constant mean curvature H-n, when the boundaries of these disks tend to infinity. This theorem generalizes to the non-zero constant mean curvature case Theorem 0.1 by Colding and Minicozzi (Ann Math 160:573-615, 2004) for minimal disks. We apply this theorem to prove the existence of a chord arc result for compact disks embedded in R-3 with constant mean curvature; this chord arc result generalizes Theorem 0.5 by Colding and Minicozzi (Ann Math 167:211-243, 2008) for minimal disks.