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Properly embedded, area-minimizing surfaces in hyperbolic 3-space. (English) Zbl 1295.53066

Summary: We prove a bridge principle at infinity for area-minimizing surfaces in the hyperbolic space \(\mathbb{H}^3\), 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.

MSC:

53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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