Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The "Wrong Minimal Surface Equation" does not have the Bernstein
  property   A celebrated result of S. Bernstein states that every solution of the minimal
surface equation over the entire plane has to be an affine linear function.
Since the paper of Bernstein appeared in 1927, many different proofs and
generalizations of this beautiful theorem were given, namely to higher
dimensions and to more general equations, for a careful account we refer to the
paper by Simo and to the monograph by Dierkes-Hildebrandt-Tromba. In his paper
Simon posed the question whether the equation \begin{equation}
(1+{u_x}^2)u_{xx}+2u_x u_y u_{xy}+ (1+{u_y}^2)u_{yy} = 0 \label{toll}
\end{equation} has the Bernstein property i.e. whether every $C^2$-solution
defined over the entire plane necessarily has to be affine. We here show by a
very simple argument that this is not the case.

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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
1
The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an