CMC-1 Surfaces in Hyperbolic and de Sitter Spaces with Cantor Ends

Castro Infantes, Ildefonso; Hidalgo, Jorge

doi:10.1007/s00009-024-02707-z

s00009-024-02707-z.pdf (577.7Ko)

Identificadores

URI: https://hdl.handle.net/10481/93920

DOI: 10.1007/s00009-024-02707-z

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Editorial

Springer Nature

Materia

CMC-1 surface

CMC-1 face

Riemann surface

Date

2024-08-05

Referencia bibliográfica

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

Patrocinador

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); Fundación Séneca, Regional Agency of Science and Technology, REF, 21899/PI/22; State Research Agency (AEI) via the Grants no. PID2020-117868GB-I00 and PID2023-150727NB-I00, funded by MCIN/AEI/10.13039/501100011033/

Résumé

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.

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