Volumes of balls in large Riemannian manifolds
Volumes of balls in large Riemannian manifolds
We prove two lower bounds for the volumes of balls in a Riemannian manifold.If (M n , g) is a complete Riemannian manifold with filling radius at least R, then it contains a ball of radius R and volume at least δ(n)R n .If (M n , hyp) is a …