Integral curvature bounds, distance estimates and applications

Abstract

In this paper we show how the classical diameter bound for manifolds with positive Ricci curvature generalizes to a situation where one has integral curvature bounds. In addition we also generalize the P. Levy isoperimetric constant to this situation. This gives generalizations of work of Lichnerow-icz, Cheng, Croke, Gallot, Colding and more. © 1998 Applied Probability Trust.