Helicoidal minimal surfaces of prescribed genus
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- 作者：David Hoffman ; Martin Traizet ; Brian White
- 关键词：2010 Math. Subj. ClassificationPrimary ; 53A10 ; Secondary ; 49Q05 ; 53C42
- 刊名：Acta Mathematica
- 出版年：2016
- 出版时间：June 2016
- 年：2016
- 卷：216
- 期：2
- 页码：217-323
- 全文大小：1,973 KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics - 出版者：Springer Netherlands
- ISSN：1871-2509
- 卷排序：216
文摘
For every genus g, we prove that \({\mathbf{S}^2\times\mathbf{R}}\) 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 \({\mathbf{S}^2}\) tends to infinity, these examples converge smoothly to complete, properly embedded minimal surfaces in \({\mathbf{R}^3}\) that are helicoidal at infinity. We prove that helicoidal surfaces in \({\mathbf{R}^3}\) of every prescribed genus occur as such limits of examples in \({\mathbf{S}^2\times\mathbf{R}}\).