Homothetical CMC surfaces in H^3 must be parabolic.
Van de Woestyne, A new characterization of the helicoids, Geometry and topology of sub- manifolds, V (Leuven/Brussels, 1992), 267ˆ a€“273, World Sci
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Homothetical surfaces with constant mean curvature in hyperbolic space
Homothetical CMC surfaces in H^3 must be parabolic.