Department of Mathematics2024-11-0920171050-692610.1007/s12220-016-9715-x2-s2.0-84976370622http://dx.doi.org/10.1007/s12220-016-9715-xhttps://hdl.handle.net/20.500.14288/7662We show that any open orientable surface can be properly embedded in H-3 as a constant mean curvature H-surface for H epsilon [0, 1). We obtain this result by proving a version of the bridge principle at infinity for H-surfaces. We also show that any open orientable surface can be nonproperly embedded in H-3 as a minimal surface.MathematicsJournal Article1559-002X404678100011Q21879