Local continuous extension of proper holomorphic maps: Low-regularity and infinite-type boundaries

We prove a couple of results on local continuous extension of proper holomorphic maps F : D -> Omega, D, Omega not subset of C-n, making local assumptions on partial derivative D and partial derivative Omega. The first result allows us to have much lower regularity, for the patches of partial derivative D, partial derivative Omega that are relevant, than in earlier results. The second result (and a result closely related to it) is in the spirit of a result by Forstneric-Rosay. However, our assumptions allow partial derivative Omega to contain boundary points of infinite type. (c) 2024 Elsevier Inc. All rights reserved.