Ricci curvature, minimal surfaces and sphere theorems

Details Ricci curvature, minimal surfaces and sphere theorems Ricci curvature, minimal surfaces and sphere theorems

1997-08-30

arxiv.org/abs/dg-ga/9709002v1

Mathematics

Differential Geometry

LaTex Form. To appear in J. Geom. Analysis

Scientific paper

Using an analogue of Myers' theorem for minimal surfaces and three
dimensional topology, we prove the diameter sphere theorem for Ricci curvature
in dimension three and a corresponding eigenvalue pinching theorem. This
settles these two open problems for closed 3 manifolds with positive Ricci
curvature since they are both false in dimensions greater than three.

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