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Improvement of the Bernstein-type theorem for space-like zero mean curvature graphs in Lorentz-Minkowski space using fluid mechanical duality

Improvement of the Bernstein-type theorem for space-like zero mean curvature graphs in Lorentz-Minkowski space using fluid mechanical duality

Calabiā€™s Bernstein-type theorem asserts that <italic>a zero mean curvature entire graph in Lorentz-Minkowski space <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="bold-italic upper L cubed"> <mml:semantics> <mml:msup> <mml:mi mathvariant="bold-italic">L</mml:mi> <mml:mn>3</mml:mn> </mml:msup> <mml:annotation encoding="application/x-tex">\boldsymbol {L}^3</mml:annotation> </mml:semantics> </mml:math> </inline-formula> which admits only space-like points is a space-like plane</italic>. Using the fluid mechanical duality between minimal ā€¦