Calculus of Variations and Geometric Measure Theory

Tobias H. Colding - C. De Lellis

Singular limit laminations, Morse index, and positive scalar curvature

created on 14 Nov 2002
modified by delellis on 27 Jun 2019


Published Paper

Inserted: 14 nov 2002
Last Updated: 27 jun 2019

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

ArXiv: math/0208100 PDF


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 S3Gamma 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).

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