Harmonic maps and constant mean curvature surfaces in H 2 x R

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Complete surfaces of constant curvature in H2 × R and S2 × R (2005, background): “An up to date reference list of papers on this subject can be found in [ 3 ].”
An asymptotic theorem for minimal surfaces and existence results for minimal graphs in $H^2 \times R$ (2007, background): “tforward veriﬁcations. 3. minimal vertical graphs There are many notions of graphs in H2 × R, but the notion of minimal vertical graphs has appeared in many important theorems. See, for instance [4], [7], [11], [12], [18], [23]. MINIMAL 11 Consider a C2 function t = u(x,y). The vertical minimal equa”
The Gauss Map of Minimal Surfaces in the Heisenberg Group (2006, methodology): “y of meromorphic and harmonic maps. More recently, I. Ferna´ndez and P. Mira proved the existence of a harmonic “hyperbolic Gauss map” into H2 for CMC 1 2 surfaces in H 2 ×Rthat are nowhere vertical ([FM07]). They also proved that any harmonic map (under a hypothesis) can be the hyperbolic Gauss map”
Half‐space theorem, embedded minimal annuli and minimal graphs in the Heisenberg group (2007, background): “When the surface is a graph, Fernandez and Mira [9] constructed a harmonic ‘hyperbolic Gauss map’ from the surface to H(2) whose associated Hopf differential is Q = −Q0.”
Totally umbilic surfaces in homogeneous 3-manifolds (2006, unknown): “See for example [14], [6], [7], [17], [15], [12], [13], [11], [9], [4], [2], [ 10 ], [5] and [8].”