Consider a Riemannian manifold \(M\) of dimension \(n\) with \(\Ric(M)\ge 0\). Then there exists a cover by balls with fixed radius \(r>0\) such that the covering multiplicity can be estimated by some constant \(C\) which depends only on the dimension \(n\).
Proof [TODO] Link to heading
The proof is not valid yet, since Gromovs packing lemma is only formulated for balls.
Apply Gromovs packing lemma with $$