Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The curve shortening flow with density of a spherical curve in
  codimension two   In the present paper we carry out a systematic study about the flow of a
spherical curve by the mean curvature flow with density in a 3-dimensional
rotationally symmetric space with density $(M^3_w,\:g_w,\:\xi)$ where the
density $\xi$ decomposes as sum of a radial part $\varphi$ and an angular part
$\psi$. We analyse how either the parabolicity or the hyperbolicity of
$(M^3_w,\:g_w)$ condition the behaviour of the flow when the solution goes to
infinity.

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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
30
The categories of this paper are: q-alg
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The categories of this paper are: stat
8
The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int