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Abstract: In this paper, we give a survey of various sphere theorems in geometry. Theseinclude the topological sphere theorem of Berger and Klingenberg as well as thedifferentiable version obtained by the authors. These theorems employ a varietyof methods, including geodesic and minimal surface techniques as well asHamilton-s Ricci flow. We also obtain here new results concerning completemanifolds with pinched curvature.



Author: S. Brendle, R.M. Schoen

Source: https://arxiv.org/



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