We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
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 ${\rm Scal}\, >0$.
