Singular limit laminations, Morse index, and positive scalar curvature

revised version: August 2002
Tobias H. Colding, and Camillo De Lellis
(Please use for correspondence this email).

Submission date: 07. Aug. 2002
Pages: 21
MSC-Numbers: 53A10, 53C21, 57N10
Keywords and phrases: minimal surfaces, morse index, positive scalar curvature, laminations
Download preprint: PDF (716 kB), PS ziped (281 kB)

Abstract:
For any 3-manifold and any nonnegative integer , we give here examples of metrics on M each of which has a sequence of embedded minimal surfaces of genus and without Morse index bounds. On any spherical space form we construct such a metric with positive scalar curvature. More generally we construct such a metric with (and such surfaces) on any 3-manifold which carries a metric with .