QUANTITATIVE VOLUME SPACE FORM RIGIDITY UNDER LOWER RICCI CURVATURE BOUND II

摘要

This is the second paper of two in a series under the same title; both study the quantitative volume space form rigidity conjecture: a closed n-manifold of Ricci curvature at least (n - 1) H, H = +/- 1 or 0 is diffeomorphic to an H-space form if for every ball of definite size on M, the lifting ball on the Riemannian universal covering space of the ball achieves an almost maximal volume, provided the diameter of M is bounded for H not equal 1.