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Let M be a complete open Riemannian manifold with nonnegative Ricci curvature outside a compact set B. We show that the following ball covering property (see [LT]) is true provided that the sectional curvature has a lower bound : For a fixed p 0 ∈M, there exist N>0 and r 0 >0 such that for r≥r 0 , there exist p 1 ,...,p k ∈∂B p0 (2r), k≤N, with ∪ j=1 k B pj (r)⊃∂B p0 (2r). Furthermore N and r 0 depend only on the dimension, the lower bound on the sectional curvature, and the radius of the ball at p 0 that contains B

Ball covering on manifolds with nonnegative Ricci curvature near infinity