Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Curves and surfaces with constant nonlocal mean curvature: meeting
  Alexandrov and Delaunay   We are concerned with hypersurfaces of $\mathbb{R}^N$ with constant nonlocal
(or fractional) mean curvature. This is the equation associated to critical
points of the fractional perimeter under a volume constraint. Our results are
twofold. First we prove the nonlocal analogue of the Alexandrov result
characterizing spheres as the only closed embedded hypersurfaces in
$\mathbb{R}^N$ with constant mean curvature. Here we use the moving planes
method. Our second result establishes the existence of periodic bands or
"cylinders" in $\mathbb{R}^2$ with constant nonlocal mean curvature and
bifurcating from a straight band. These are Delaunay type bands in the nonlocal
setting. Here we use a Lyapunov-Schmidt procedure for a quasilinear type
fractional elliptic equation.

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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex