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.

See also

Minimal Surface

Explore with Wolfram|Alpha


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 Theorem

Cite this as:

Weisstein, Eric W. "Bernstein Minimal Surface Theorem." From MathWorld--A Wolfram Web Resource.

Subject classifications