Helicoidal minimal surfaces of prescribed genus

• 成果类型: Article
• 署名作者: Hoffman, David; Traizet, Martin; White, Brian
• 署名单位: Stanford University; Universite de Tours
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-016-0139-z
• 发表日期: 2016
• 页码: 217-323
• 关键词: bridge principle; CURVATURE; 3-manifolds

摘要

For every genus g, we prove that contains complete, properly embedded, genus-g minimal surfaces whose two ends are asymptotic to helicoids of any prescribed pitch. We also show that as the radius of the tends to infinity, these examples converge smoothly to complete, properly embedded minimal surfaces in that are helicoidal at infinity. We prove that helicoidal surfaces in of every prescribed genus occur as such limits of examples in .