*Published Paper*

**Inserted:** 14 nov 2002

**Last Updated:** 27 jun 2019

**Journal:** Topology

**Volume:** 44

**Number:** 1

**Pages:** 25-45

**Year:** 2003

**Abstract:**

For any 3-manifold M and any nonnegative integer g, we give here examples of
metrics on M each of which has a sequence of embedded minimal surfaces of genus
g and without Morse index bounds. On any spherical space form S^{3Gamma}* we
construct such a metric with positive scalar curvature. More generally we
construct such a metric with Scal>0 (and such surfaces) on any 3-manifold which
carries a metric with Scal>0. In all but one of these examples the Hausdorff
limit will be a singular minimal lamination. The singularities being in each
case exactly two points lying on a closed leaf (the leaf is a strictly stable
sphere).
*

**Keywords:**
minimal surfaces, Morse index, positive scalar curvature, laminations