Bernstein Minimal Surface Theorem

If a Minimal Surface is given by the equation $z=f(x,y)$ and $f$ has Continuous first and second Partial Derivatives for all Real $x$ and $y$, then $f$ is a Plane.

References

Hazewinkel, M. (Managing Ed.). Encyclopaedia of Mathematics: An Updated and Annotated Translation of the Soviet ``Mathematical Encyclopaedia.'' Dordrecht, Netherlands: Reidel, p. 369, 1988.