Abstract
where f: MO M1 is a homeomorphism and dil f is the dilatation of f given by dil f = supX,X2 dist(f(x) , f(x2))/ dist(x1, x2) . If MO and M1 are not homeomorphic, define dL(MO, MI) = +oo. Gromov [20] proves the remarkable result that the space of compact Riemannian manifolds f((A, 3, D) of sectional curvature IKI 3 > 0, and diameter dM v, and diameter dM c(IKI , dm, VM1) In particular, Gromov's compactness theorem may be strengthened to the statement that f((A, v , D) is C1 'l compact in the Lipschitz topology. In this paper, we study the question of Lipschitz convergence of compact Riemannian manifolds with bounds imposed on the Ricci curvature Ric in
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