Abstract
We prove a bridge principle at infinity for area-minimizing surfaces in the hyperbolic $\mathbb{H}^3$, and we use it to prove that any open, connected, orientable surface can be properly embedded in $\mathbb{H}^3$as an area-minimizing surface. Moreover, the embedding can be constructed in such a way that the limit sets of different ends are disjoint.
Citation
Francisco Martín. Brian White. "Properly embedded, area-minimizing surfaces in hyperbolic 3-space." J. Differential Geom. 97 (3) 515 - 544, July 2014. https://doi.org/10.4310/jdg/1406033978
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