Bernstein's problem

This article is about the Bernstein problem for minimal surfaces. For the analogous problem for maximal surfaces, see Bernstein problem for maximal surfaces. For Bernstein's problem in mathematical genetics, see Genetic algebra. For Bernstein's degrees-of-freedom problem in motor control, see Degrees of Freedom Problem (Motor Control). For its possible generalization in global differential geometry, see spherical Bernstein's problem.

In differential geometry, Bernstein's problem is as follows: if the graph of a function on Rn−1 is a minimal surface in Rn, does this imply that the function is linear? This is true for n at most 8, but false for n at least 9. The problem is named for Sergei Natanovich Bernstein who solved the case n = 3 in 1914.

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