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Gluing diffeomorphisms, bi-Lipschitz mappings and homeomorphisms
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Paper
Gluing diffeomorphisms, bi-Lipschitz mappings and homeomorphisms
2025
Overview
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.
Publisher
Cornell University Library, arXiv.org
Subject
