A direct proof of Gromov's theorem

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 curvatures K_σ do not exceed C, and their injectivity radii are at least 1/C, then 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.