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Singular limit laminations, Morse index, and positive scalar curvature

Tobias H. Colding·Camillo De Lellis
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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^3/Gamma 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).

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Tobias H. Colding, Camillo De Lellis. 2002-08-14. Singular limit laminations, Morse index, and positive scalar curvature. https://arxiv.org/abs/math/0208100

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