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In this paper, we show that any open orientable surface S can be properlyembedded in H^3 as a minimizing H-surface for any 0<=H<1. We obtained thisresult by proving a version of the bridge principle at infinity for H-surfaces.We also show that any open orientable surface S can be nonproperly embedded inH^3 as a minimal surface, too.

$H$-Surfaces with Arbitrary Topology in Hyperbolic 3-Space