Non-proper helicoid-like limits of closed minimal surfaces in 3-manifolds

Abstract

We show that there exists a metric with positive scalar curvature on S 2 × 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.