An embedded genus-one helicoid

• 成果类型: Article
• 署名作者: Weber, Matthias; Hoffman, David; Wolf, Michael
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2009.169.347
• 发表日期: 2009
• 页码: 347-448
• 关键词: minimal-surfaces; fixed genus; SPACE; ends; TOPOLOGY; uniqueness; CURVATURE; handles; disks

摘要

There exists a properly embedded minimal surface of genus one with one end. The end is asymptotic to the end of the helicoid. This genus one helicoid is constructed as the limit of a continuous one-parameter family of screw-motion invariant minimal surfaces-also asymptotic to the helicoid-that have genus equal to one in the quotient.