We show a global representation formula for a certain kind of Weingarten surface in hyperbolic three-space, which is based on the formula due to Gálvez, Martínez and Milán.
As an application of the representation formula, we also investigate surfaces with harmonic-mean curvature one (HMC-1 surfaces).
We allow them to have certain kinds of singularities, and discuss some global properties.
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