QLunch: The Bernstein Theorem – University of Copenhagen

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QLunch: The Bernstein Theorem

Speaker: Francesco Chini from QMATH

Title: The Bernstein Theorem

I will give a brief introduction to minimal surfaces and I will show the classical Bernstein theorem about the non-existence of nontrivial entire solutions for the minimal surface equation in dimension 2. This result is actually true for n less than 8 and false in higher dimensions. However, with some extra assumptions on the growth of the solution, it is possible to extend the result to any dimension.

I will show a very elegant proof by J\"urgen Moser of a Bernstein theorem
of this kind, using the Harnack inequality for elliptic equations. 

If there will still be time, I will present some connections with some types of
solitons of the mean curvature flow.