ScalingStacks

Lemma 5.12. Let $(M^{2n},g)$ be a closed Riemannian manifold with $Ric(g)\geq 0$, let $p\in M$and $1<R\leq diam(X,g)$. Then $\frac{R-1}{4n}\leq\frac{\text{Vol}(B(p,2(R+1)))}{\text{Vol}(B(p,1))}$.