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

• Antonio Alarcón ^[1] ; Franc Forstnerič ^[2]
  1. [1] Universidad de Granada

     Universidad de Granada

     Granada, España

     
  2. [2] University of Ljubljana

     University of Ljubljana

     Eslovenia

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 37, Nº 4, 2021, págs. 1399-1412
• Idioma: inglés
• DOI: 10.4171/rmi/1231
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.