Resumen de The Calabi–Yau problem for Riemann surfaces with finite genus and countably many ends

Antonio Alarcón López , Franc Forstneric

• In this paper, we show that if R is a compact Riemann surface and M=R∖⋃iDi is a domain in R whose complement is a union of countably many pairwise disjoint smoothly bounded closed discs, Di, then there is a complete conformal minimal immersion X:M→R3, extending to a continuous map X:M¯¯¯¯¯→R3, such that X(bM)=⋃iX(bDi) is a union of pairwise disjoint Jordan curves. In particular, M is the complex structure of a complete bounded minimal surface in R3. This extends a recent result for finite bordered Riemann surfaces.