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MiS Preprint
66/2002
Singular limit laminations, Morse index, and positive scalar curvature
Tobias H. Colding and Camillo De Lellis
Abstract
For any $3$-manifold $M^3$ and any nonnegative integer ${\bf{g}}$, we give here examples of metrics on $M$ each of which has a sequence of embedded minimal surfaces of genus ${\bf{g}}$ and without Morse index bounds. On any spherical space form ${\bf S}^3/\Gamma$ we construct such a metric with positive scalar curvature. More generally we construct such a metric with ${\rm Scal}\, >0$ (and such surfaces) on any $3$-manifold which carries a metric with ${\rm Scal}\, >0$.
