A direct proof of Gromov’s theorem

Abstract

A new proof of a theorem by Gromov is given: for any positive C and any integer n greater than 1, there exists a function Δ C,n (δ) such that if the Gromov–Hausdorff distance between two complete Riemannian n-manifolds V and W is at most δ, their sectional curvaturcs |K σ | do not exceed C, and their injectivity radii are at least 1/C, than the Lipschitz distance between V and W is less than Δ C,n (δ), and Δ C,n (δ) → 0 as δ → 0. Bibliography: 6 titles.