Abstract
In this note, we show that a complete n-dim Riemannian manifold with nonnegative Ricci curvature is of finite topological type provided that the diameter growth of M is of order \(o(r^{((n-1)\alpha +1)/n})\) and the sectional curvature is no less than \(-{\frac{c}{r^{2\alpha }}}\) (here, \(0 \le \alpha \le 1\) and c is some positive constant) outside a geodesic ball large enough. In particular, if in a neighborhood of an isolated end of the manifold in question, the above assumptions are satisfied, then the end has a collared neighborhood.
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We thank the referee for his/her valuable suggestion.
Partially supported by NSF of China (No. 11571228).
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Jiang, H., Yang, YH. Diameter growth and bounded topology of complete manifolds with nonnegative Ricci curvature. Ann Glob Anal Geom 51, 359–366 (2017). https://doi.org/10.1007/s10455-016-9539-8
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DOI: https://doi.org/10.1007/s10455-016-9539-8