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arXiv · 0904.2604

Sphere Theorems in Geometry

S. Brendle·R. M. Schoen
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Abstract

In this paper, we give a survey of various sphere theorems in geometry. These include the topological sphere theorem of Berger and Klingenberg as well as the differentiable version obtained by the authors. These theorems employ a variety of methods, including geodesic and minimal surface techniques as well as Hamilton's Ricci flow. We also obtain here new results concerning complete manifolds with pinched curvature.

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S. Brendle, R. M. Schoen. 2009-07-01. Sphere Theorems in Geometry. https://arxiv.org/abs/0904.2604

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