2024/04/21 by Paweł Goldstein, Goldstein, Paweł, Zofia Grochulska +3
Mathematics · Physics and Astronomy · #58C07 #58C25 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Geometric Topology (math.GT) #Nonlinear Waves and Solitons #Primary: 54C20 Secondary: 57N55
paper · pdf · doi:10.48550/arxiv.2404.13508
openalex publication_date 2024/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.