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.

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.
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