MANIFOLDS WITH LOWER RICCI AND L¹-SECTIONAL CURVATURE CONTROL.

Suppose that a sequence of Riemannian manifolds with Ricci curvature ≥ -k2 converges to a Gromov-Hausdorff limit X. We show that if the amount of sectional curvature below K of the limiting manifolds approaches 0 in a suitable L1-sense, then X is an Alexandrov space of curvature ≥ K. As applications we present several generalizations of classical theorems. [ABSTRACT FROM AUTHOR]