Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gradient estimates for mean curvature flow with Neumann boundary
  conditions   We study the mean curvature flow of graphs both with Neumann boundary
conditions and transport terms. We derive boundary gradient estimates for the
mean curvature flow. As an application, the existence of the mean curvature
flow of graphs is presented. A key argument is a boundary monotonicity formula
of a Huisken type derived using reflected backward heat kernels. Furthermore,
we provide regularity conditions for the transport terms.

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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
3
The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat