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

  1. Antonio Alarcón 1
  2. Franc Forstnerič 2
  1. 1 Universidad de Granada
    info

    Universidad de Granada

    Granada, España

    ROR https://ror.org/04njjy449

  2. 2 University of Ljubljana
    info

    University of Ljubljana

    Liubliana, Eslovenia

    ROR https://ror.org/05njb9z20

Journal:
Revista matemática iberoamericana

ISSN: 0213-2230

Year of publication: 2021

Volume: 37

Issue: 4

Pages: 1399-1412

Type: Article

DOI: 10.4171/RMI/1231 DIALNET GOOGLE SCHOLAR

More publications in: Revista matemática iberoamericana

Abstract

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.

Data source: Dialnet