Existence of embedded space-like maximal graphs containing entire null lines in Lorentz-Minkowski 3-space, plus rigidity: any such graph over a convex domain must be a light-like plane.
Improvement of the Bernstein-type theorem for space-like zero mean curvature graphs in Lorentz-Minkowski space using fluid mechanical duality
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Calabi's Bernstein-type theorem asserts that a zero mean curvature entire graph in Lorentz-Minkowski space $\boldsymbol L^3$ which admits only space-like points is a space-like plane. Using the fluid mechanical duality between minimal surfaces in Euclidean 3-space $\boldsymbol E^3$ and maximal surfaces in Lorentz-Minkowski space $\boldsymbol L^3$, we give an improvement of this Bernstein-type theorem. More precisely, we show that a zero mean curvature entire graph in $\boldsymbol L^3$ which does not admit time-like points (namely, a graph consists of only space-like and light-like points) is a plane.
fields
math.DG 2years
2019 2verdicts
UNVERDICTED 2representative citing papers
An entire zero mean curvature graph in R^{n+1}_1 consisting only of space-like or light-like points is a hyperplane.
citing papers explorer
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Space-like maximal surfaces containing entire null lines in Lorentz-Minkowski 3-space
Existence of embedded space-like maximal graphs containing entire null lines in Lorentz-Minkowski 3-space, plus rigidity: any such graph over a convex domain must be a light-like plane.
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Bernstein-type theorem for zero mean curvature hypersurfaces without time-like points in Lorentz-Minkowski space
An entire zero mean curvature graph in R^{n+1}_1 consisting only of space-like or light-like points is a hyperplane.