Sphere Theorems in Geometry

Details Sphere Theorems in Geometry Sphere Theorems in Geometry

2009-04-16

arxiv.org/abs/0904.2604v2

Mathematics

Differential Geometry

Some typos corrected; to appear in Surveys in Differential Geometry

Scientific paper

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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