Embedding bordered Riemann surfaces in strongly pseudoconvex domains

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 C n , 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 .