Gluing diffeomorphisms, bi-Lipschitz mappings and homeomorphisms
| Autor: | Goldstein, Paweł, Grochulska, Zofia, Hajłasz, Piotr |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In the paper, we address the following problem, often encountered in geometric constructions: having defined an orientation preserving diffeomorphism in a number of `patches' on a manifold $\mathcal{M}$, can we extend it to a diffeomorphism of the whole manifold $\mathcal{M}$? We give a positive answer, provided the `patches' are sufficiently regular. Then, we extend the same result to the case of bi-Lipschitz homeomorphisms and homeomorphisms. |
| Databáze: | arXiv |
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