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Singular limit laminations, Morse index, and positive scalar curvature


Colding, T; De Lellis, C (2005). Singular limit laminations, Morse index, and positive scalar curvature. Topology, 44(1):25-45.

Abstract

For any 3-manifold M3 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 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.

Abstract

For any 3-manifold M3 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 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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Minimal surfaces; Morse index; Positive scalar curvature; Laminations
Language:English
Date:2005
Deposited On:19 Feb 2010 15:18
Last Modified:06 Dec 2017 20:46
Publisher:Elsevier
ISSN:0040-9383
Publisher DOI:https://doi.org/10.1016/j.top.2004.01.007

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