Resumen de The Calabi–Yau problem for minimal surfaces with Cantor ends

Franc Forstneric

• We show that every connected compact or bordered Riemann surface contains a Cantor set whose complement admits a complete conformal minimal immersion in R3 with bounded image. The analogous result holds for holomorphic immersions into any complex manifold of dimension at least 2, for holomorphic null immersions into Cn with n 3, for holomorphic Legendrian immersions into an arbitrary complex contact manifold, and for superminimal immersions into any selfdual or anti-self-dual Einstein four-manifold.