Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gradient Estimates of Mean Curvature Equation with Neumann Boundary
  Condition in $ M^n\times \mathbb{R}$   In this note, we study the prescribed mean curvature equation with
  Neumann boundary conditions on Riemannian product manifold $ M^n\times
\mathbb{R}$. The main goal is to establish the boundary gradient estimates for
solutions by the maximum principle.
  As a consequence, we obtain an existence result.

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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio