Ball Covering on Manifolds With Nonnegative Ricci Curvature Near Infinity

Abstract

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 po G M, there exist N > 0 and r0 > 0 such that for r > r$ , there exist px, ... , pk € dBPo(2r), k < N , with *: \jBPj(r)DdBPQ(2r). j-lFurthermore N and r0 depend only on the dimension, the lower bound on the sectional curvature, and the radius of the ball at p0 that contains B .