Non-proper helicoid-like limits of closed minimal surfaces in 3-manifolds. (English) Zbl 1161.53043
Summary: We show that there exists a metric with positive scalar curvature on \(\mathbf S^{2} \times \mathbf S^{1}\) and a sequence of embedded minimal cylinders that converges to a minimal lamination that, in a neighborhood of a strictly stable 2-sphere, is smooth except at two helicoid-like singularities on the 2-sphere. The construction is inspired by a recent example by D. Hoffman and B. White.
MSC:
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
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