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- Title
Diameter growth and bounded topology of complete manifolds with nonnegative Ricci curvature.
- Authors
Jiang, Huihong; Yang, Yi-Hu
- 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.
- Subjects
TOPOLOGY; MANIFOLDS (Mathematics); CURVATURE; NONNEGATIVE matrices; RICCI flow
- Publication
Annals of Global Analysis & Geometry, 2017, Vol 51, Issue 4, p359
- ISSN
0232-704X
- Publication type
Article
- DOI
10.1007/s10455-016-9539-8