The Calabi-Yau problem for minimal surfaces with Cantor endsForstnerič, Franc (Avtor) minimal surfacesCalabi–Yau problemnull curveLegendrian curveWe show that every connected compact or bordered Riemann surface contains a Cantor set whose complement admits a complete conformal minimal immersion in ${\mathbb R}^3$ with bounded image. The analogous result holds for holomorphic immersions into any complex manifold of dimension at least $2$, for holomorphic null immersions into ${\mathbb C}^n$ with $n \ge 3$, for holomorphic Legendrian immersions into an arbitrary complex contact manifold, and for superminimal immersions into any selfdual or anti-self-dual Einstein four-manifold.20232024-04-08 11:06:17Neznano18630sl