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→Ω, D,Ω⊊Cn, making local assumptions on ∂D and ∂Ω. The first result allows us to have much lower regularity, for the patches of ∂D,∂Ω 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 Forstnerič–Rosay. However, our assumptions allow ∂Ω to contain boundary points of infinite type.