CMC-1 Surfaces in Hyperbolic and de Sitter Spaces with Cantor Ends Castro Infantes, Ildefonso Hidalgo, Jorge CMC-1 surface CMC-1 face Riemann surface We prove that on every compact Riemann surface M, there is a Cantor set C ⊂ M such that M\C admits a proper conformal constant mean curvature one (CMC-1) immersion into hyperbolic 3-space H3. Moreover, we obtain that every bordered Riemann surface admits an almost proper CMC-1 face into de Sitter 3-space S31, and we show that on every compact Riemann surface M, there is a Cantor set C ⊂ M such that M\C admits an almost proper CMC-1 face into S31. These results follow from different uniform approximation theorems for holomorphic null curves in C2 × C* that we also establish in this paper. 2024-09-04T10:30:19Z 2024-09-04T10:30:19Z 2024-08-05 journal article Castro-Infantes, I., Hidalgo, J. CMC-1 Surfaces in Hyperbolic and de Sitter Spaces with Cantor Ends. Mediterr. J. Math. 21, 167 (2024). https://doi.org/10.1007/s00009-024-02707-z https://hdl.handle.net/10481/93920 10.1007/s00009-024-02707-z eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Springer Nature