For complete spacelike CMC H surfaces in isotropic 3-space, nonconstant Gaussian curvature attains every value below H^2, and constant-curvature surfaces are exactly the listed quadrics.
Calabi, Examples of Bernstein problems for some nonlinear equations , in Global Analysis (Proc
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Bernstein-type theorem for constant mean curvature surfaces in the isotropic 3-space
For complete spacelike CMC H surfaces in isotropic 3-space, nonconstant Gaussian curvature attains every value below H^2, and constant-curvature surfaces are exactly the listed quadrics.