# Bernstein's minimal surface problem

Does anyone know some good reference for this? For your convenience, here's the Wikipedia page on it, on which you can find the statement and the problem proposed: http://en.wikipedia.org/wiki/Bernstein%27s_problem

Specifically, I'm looking for:

• A good solution on the case n=3, i.e the case that Bernstein proved that a graph of a real function on $R^2$ that is also a minimal surface in $R^3$ must be a plane.

• Some additional information, e.g usage of the theorem, history etc.

• (If possible) a proof why the statement is true in dimensions at most 8 but false in dimensions at least 9.

I've looked around online a decent amount of time and found a few papers, including ones by WY Hsiang and P Tomter, but was wondering if there were more than that written on the topic.

Thanks for any help!

-
Welcome to Math.SE! The first bullet item is covered in: Nitsche, Johannes C. C. Elementary proof of Bernstein's theorem on minimal surfaces, Ann. of Math. (2) 66 (1957), 543–544. JSTOR link. (NB: a 2-page paper in the Annals of Math.) // If you have access to MathSciNet, this review of the Bombieri-De Giorgi-Giusti paper covers the main historical points. –  user53153 Jan 8 '13 at 2:51
Wonderful, thank you! –  SGh Jan 8 '13 at 3:06