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arXiv · 0802.0098

A direct proof of one Gromov's theorem

Yu. D. Burago·S. G. Malev·D. Novikov
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Abstract

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 $δ\to 0$.

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Yu. D. Burago, S. G. Malev, D. Novikov. 2008-02-01. A direct proof of one Gromov's theorem. https://arxiv.org/abs/0802.0098

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