If a minimal surface is given by the equation 
and 
has continuous first and second partial
derivatives for all real 
and 
, then 
is a plane.
Bernstein Minimal Surface Theorem
See also
Minimal SurfaceExplore with Wolfram|Alpha
References
Hazewinkel, M. (Managing Ed.). Encyclopaedia of Mathematics: An Updated and Annotated Translation of the Soviet "Mathematical Encyclopaedia." Dordrecht, Netherlands: Reidel, p. 369, 1988.Osserman, R. "Bernstein's Theorem." §5 in A Survey of Minimal Surfaces. New York: Dover, pp. 34-42, 1986.Referenced on Wolfram|Alpha
Bernstein Minimal Surface TheoremCite this as:
Weisstein, Eric W. "Bernstein Minimal Surface Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BernsteinMinimalSurfaceTheorem.html