@misc{10481/91878,
year = {2024},
month = {2},
url = {https://hdl.handle.net/10481/91878},
abstract = {We prove that every open Riemann surface M is the complex structure of a complete surface of constant mean curvature 1 (CMC-1) in the 3-dimensional hyperbolic space H3. We go further and establish a jet interpolation theorem for complete conformal CMC-1 immersions M→H3. As a consequence, we show the existence of complete densely immersed CMC-1 surfaces in H3 with arbitrary complex structure. We obtain these results as application of a uniform approximation theorem with jet interpolation for holomorphic null curves in C2×C∗ which is also established in this paper.},
organization = {State
Research Agency (AEI) via the grant no. PID2020-117868GB-I00},
organization = {“Maria
de Maeztu” Excellence Unit IMAG, reference CEX2020-001105-M, funded by
MCIN/AEI/10.13039/501100011033/, Spain},
organization = {Grant PID2021-124157NB-I00 funded
by MCIN/AEI/10.13039/501100011033/ ‘ERDF A way of making Europe’, Spain},
organization = {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), by Fundación Séneca, Regional Agency of Science and
Technology, REF, 21899/PI/22},
keywords = {Constant mean curvature surface},
keywords = {Bryant surface},
keywords = {Regular end},
title = {Complete CMC-1 surfaces in hyperbolic space with arbitrary complex structure},
doi = {10.1142/S0219199724500111},
author = {Alarcón López, Antonio and Castro Infantes, Ildefonso and Hidalgo, Jorge},
}