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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 ${\rm Scal}\, >0$.

Received:
Aug 7, 2002
Published:
Aug 7, 2002
MSC Codes:
53A10, 53C21, 57N10
Keywords:
minimal surfaces, morse index, positive scalar curvature, laminations

Related publications

inJournal
2005 Repository Open Access
Tobias H. Colding and Camillo De Lellis

Singular limit laminations, Morse index, and positive scalar curvature

In: Topology, 44 (2005) 1, pp. 25-45