Complete CMC-1 surfaces in hyperbolic space with arbitrary complex structure
| Autor: | Alarcon, Antonio, Castro-Infantes, Ildefonso, Hidalgo, Jorge |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Commun. Contemp. Math. (2024) 2450011 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1142/S0219199724500111 |
| Popis: | 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 $\mathbb{H}^3$. We go further and establish a jet interpolation theorem for complete conformal CMC-1 immersions $M\to \mathbb{H}^3$. As a consequence, we show the existence of complete densely immersed CMC-1 surfaces in $\mathbb{H}^3$ with arbitrary complex structure. We obtain these results as application of a uniform approximation theorem with jet interpolation for holomorphic null curves in $\mathbb{C}^2\times\mathbb{C}^*$ which is also established in this paper. Comment: To appear in Commun. Contemp. Math |
| Databáze: | arXiv |
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