A direct proof of one Gromov's theorem

Burago, Yu. D.; Malev, S. G.; Novikov, D.

A direct proof of one Gromov's theorem

Authors

Burago, Yu. D.

Malev, S. G.

Novikov, D.

Description

We give a new proof of the Gromov theorem: For any $C>0$ and integer $n>1$ there exists a function $Δ_{C,n}$ such that if the Gromov--Hausdorff distance between complete Riemannian $n$-manifolds $V$ and $W$ is not greater than $δ$, absolute values of their sectional curvatures $|K_σ|\leq C$, and their injectivity radii $\geq 1/C$, then the Lipschitz distance between $V$ and $W$ is less than $Δ_{C,n}(δ)$ and $Δ_{C,n}\to 0$ as $δ\to 0$.