Embedding Bordered Riemann Surfaces in Strongly Pseudoconvex Domains
FRANC FORSTNERIˇC
Abstract:We show that every bordered Riemann surface, M, with smooth boundary bM admits a proper holomorphic map M → Ω into any bounded strongly pseudoconvex domain Ω in Cn, n > 1, extending to a smooth map f : M → Ω which can be chosen an immersion if n ≥ 3 and an embedding if n ≥ 4. Furthermore, f can be chosen to approximate a given holomorphic map M → Ω on compacts in M and interpolate it at finitely many given points in M.
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.