Abstract
We prove that the ends of a properly immersed simply or one connected minimal surface in \({{\mathbb{H}} \times {\mathbb{R}}}\) contained in a slab of height less than \({\pi}\) of \({{\mathbb{H}} \times {\mathbb{R}}}\) are multi-graphs. When such a minimal surface is properly embedded, then the ends are graphs. When such a minimal surface is properly embedded and simply connected, it is an entire graph.
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P. Collin, L. Hauswirth, and H. Rosenberg was partially supported by the ANR-11-IS01-0002 Grant.
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Collin, P., Hauswirth, L. & Rosenberg, H. Properly immersed minimal surfaces in a slab of \({\mathbb {H} \times {\mathbb {R}}}\), \({\mathbb {H}}\) the hyperbolic plane. Arch. Math. 104, 471–484 (2015). https://doi.org/10.1007/s00013-015-0744-7
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DOI: https://doi.org/10.1007/s00013-015-0744-7