## Complete manifolds with nonnegative Ricci curvature and quadratically nonnegatively curved infinity.(English)Zbl 0901.53023

Let $$M$$ be a complete, noncompact Riemannian manifold. For any $$r>0$$, let $$K_p(r):=\inf K$$ on $$M\setminus B_r(p)$$, where $$B_r(p)$$ is the geodesic ball of radius $$r$$ around $$p\in M$$, $$k$$ denotes the sectional curvature of $$M$$, and the infimum is taken over all the sections at all points on $$M\setminus B_r(p)$$.
The authors suppose $$M$$ with nonnegative Ricci curvature and $$K_p(r)\geq-C/(1+r^2)$$ for some constant $$C>0$$. They obtain some topological finiteness theorems for $$M$$ satisfying above conditions and some additional conditions on the volume growth.

### MSC:

 53C20 Global Riemannian geometry, including pinching 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
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