Calculus of Variations and Geometric Measure Theory
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T. Colding - C. De Lellis

Singular limit laminations, Morse index, and positive scalar curvature

created on 14 Nov 2002
modified by delellis on 03 May 2011


Published Paper

Inserted: 14 nov 2002
Last Updated: 3 may 2011

Journal: Topology
Volume: 44
Number: 1
Pages: 25-45
Year: 2003


For any 3-manifold $M^3$ 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 $Scal>0$.

For the most updated version and eventual errata see the page


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

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