The graph t = arcsinh(e^y cos x) is an entire mixed-type zero-mean curvature graph in Lorentz-Minkowski space that is not a Kobayashi surface.
Calabi, Examples of Bernstein problems for some nonlinear equation s, Proc
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Examples of entire zero-mean curvature graphs of mixed-type in Lorentz-Minkowski space via Konderak's formulas
The graph t = arcsinh(e^y cos x) is an entire mixed-type zero-mean curvature graph in Lorentz-Minkowski space that is not a Kobayashi surface.