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2002
Issue 66

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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 $g$ , 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 $S^{3} / Γ$ we construct such a metric with positive scalar curvature. More generally we construct such a metric with $S c a l > 0$ (and such surfaces) on any $3$ -manifold which carries a metric with $S c a l > 0$ .

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Received:: 07.08.02

Published:: 07.08.02

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

BibTex DOI: 10.1016/j.top.2004.01.007 ArXiv: math/0208100