Manifolds of positive Ricci curvature with almost maximal volume
Manifolds of positive Ricci curvature with almost maximal volume
PERELMAN 10.In this note we consider complete Riemannian manifolds with Ricci curvature bounded from below.The well-known theorems of Myers and Bishop imply that a manifold M n with Ric ~ n -1 satisfies diam(1l1 n ) ~ diam(Sn(I)), Vol(Mn) ~ Vol(Sn(I)).It follows from [Ch] that equality in either of these …