Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimal Graphs in Nil_3 : existence and non-existence results   We study the minimal surface equation in the Heisenberg space, Nil_3. A
geometric proof of non existence of minimal graphs over non convex, bounded and
unbounded domains is achieved (our proof holds in the Euclidean space as well).
We solve the Dirichlet problem for the minimal surface equation over bounded
and unbounded convex domains, taking bounded, piecewise continuous boundary
value. We are able to construct a Scherk type minimal surface and we use it as
a barrier to construct non trivial minimal graphs over a wedge of angle between
\pi/2 ,and \pi taking non negative continuous boundary data, having at least
quadratic growth. In the case of an half- plane, we are also able to give
solutions (with either linear or quadratic growth), provided some geometric
hypothesis on the boundary data. Finally, some open problem arising from our
work, are posed.

19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph