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On manifolds with lower quadratic curvature decay and volume pinching. (English) Zbl 1462.53024

For a complete noncompact Riemannian manifold with lower quadratic curvature decay, the authors give some conditions to have finite topological type. Most of curvature conditions are much weaker than the assumptions in [J. Lott, Math. Ann. 325, No. 3, 525–541 (2003; Zbl 1034.53033); J. Sha and Z. Shen, Am. J. Math. 119, No. 6, 1399–1404 (1997; Zbl 0901.53023)], so results can be viewed as natural generalizations of those works.

MSC:

53C20 Global Riemannian geometry, including pinching
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