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arXiv · dg-ga/9709002

Ricci curvature, minimal surfaces and sphere theorems

Ying Shen·Shunhui Zhu
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Abstract

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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Ying Shen, Shunhui Zhu. 1997-08-30. Ricci curvature, minimal surfaces and sphere theorems. https://arxiv.org/abs/dg-ga/9709002

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