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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!

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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
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