arXiv:0904.2604 Abstract | arXiv Analytics

arXiv:0904.2604 [math.DG]Abstract References Reviews Resources

Sphere Theorems in Geometry

Published 2009-04-16, updated 2009-07-01Version 2

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.

Comments: Some typos corrected; to appear in Surveys in Differential Geometry

Categories: math.DG, math.AP

Keywords: minimal surface techniques, results concerning complete manifolds, hamiltons ricci flow, topological sphere theorem, theorems employ

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