Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Area-minimizing ruled graphs and the Bernstein problem in the Heisenberg
  group   In this paper, we give a necessary and sufficient condition for a graphical
strip in the Heisenberg group $\mathbb{H}$ to be area-minimizing in the slab
$\{-1<x<1\}$. We show that our condition is necessary by introducing a family
of deformations of graphical strips based on varying a vertical curve. We show
that it is sufficient by showing that strips satisfying the condition have
monotone epigraphs. We use this condition to show that any area-minimizing
ruled entire intrinsic graph in the Heisenberg group is a vertical plane and to
find a boundary curve that admits uncountably many fillings by area-minimizing
surfaces.

19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
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The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an