A direct proof of one Gromov's theorem
| Autor: | Burago, Yu. D., Malev, S. G., Novikov, D. |
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| Rok vydání: | 2008 |
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| Druh dokumentu: | Working Paper |
| Popis: | We give a new proof of the Gromov theorem: For any $C>0$ and integer $n>1$ there exists a function $\Delta_{C,n}$ such that if the Gromov--Hausdorff distance between complete Riemannian $n$-manifolds $V$ and $W$ is not greater than $\delta$, absolute values of their sectional curvatures $|K_{\sigma}|\leq C$, and their injectivity radii $\geq 1/C$, then the Lipschitz distance between $V$ and $W$ is less than $\Delta_{C,n}(\delta)$ and $\Delta_{C,n}\to 0$ as $\delta\to 0$. |
| Databáze: | arXiv |
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