@misc{10481/93920,
year = {2024},
month = {8},
url = {https://hdl.handle.net/10481/93920},
abstract = {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.},
organization = {Grant PID2021-124157NB-I00 funded by MCIN/AEI/10.13039/501100011033/‘ERDF A way of making Europe’, Spain; and by Comunidad Autónoma de la Región de Murcia, Spain, within the framework of the Regional Programme in Promotion of the Scientific and Technical Research (Action Plan 2022)},
organization = {Fundación Séneca, Regional Agency of Science and Technology, REF, 21899/PI/22},
organization = {State Research Agency (AEI) via the Grants no. PID2020-117868GB-I00 and PID2023-150727NB-I00, funded by MCIN/AEI/10.13039/501100011033/},
publisher = {Springer Nature},
keywords = {CMC-1 surface},
keywords = {CMC-1 face},
keywords = {Riemann surface},
title = {CMC-1 Surfaces in Hyperbolic and de Sitter Spaces with Cantor Ends},
doi = {10.1007/s00009-024-02707-z},
author = {Castro Infantes, Ildefonso and Hidalgo, Jorge},
}