Asymptotic and local rigidity under sectional curvature bounds 

 - Bangalore:  Department of Mathematics, Indian Institute of Science:  2006 
 - Let (M, g) be a simply-connected complete Riemannian manifold of dimension ≥ 3. Suppose that the sectional curvature K satisfies −1−s(r) ≤ K ≤ −1, where r denotes distance to a fixed point in M. We prove that if lim r→∞ e 2rs(r) = 0, then (M, g) has to be 
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