$\mathrm{CMC}\text{-}1$ surfaces in hyperbolic and de Sitter spaces with Cantor ends

Ildefonso Castro-Infantes, Jorge Hidalgo

We prove that on every compact Riemann surface $M$ there is a Cantor set $C\subset M$ such that $M\setminus C$ admits a proper conformal constant mean curvature one ($\mathrm{CMC…