Gluing diffeomorphisms, bi-Lipschitz mappings and homeomorphisms

Paweł Goldstein; Zofia Grochulska; Piotr Hajłasz

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arXiv · 2404.13508

Gluing diffeomorphisms, bi-Lipschitz mappings and homeomorphisms

Paweł Goldstein·Zofia Grochulska·Piotr Hajłasz

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Abstract

Cerf and Palais independently proved a remarkable result about extending diffeomorphisms defined on smooth balls in a manifold to global diffeomorphisms of the manifold onto itself. We explain Palais' argument and show how to extend it to the class of homeomorphisms and bi-Lipschitz homeomorphisms. While Palais' argument is surprising, it is elementary and short. However, its extension to bi-Lipschitz homeomorphisms and homeomorphisms requires deep results: the stable homeomorphism and the annulus theorems.

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Paweł Goldstein, Zofia Grochulska, Piotr Hajłasz. 2024-04-21. Gluing diffeomorphisms, bi-Lipschitz mappings and homeomorphisms. https://arxiv.org/abs/2404.13508

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