Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity of free boundary minimal surfaces in locally polyhedral
  domains   We prove an Allard-type regularity theorem for free-boundary minimal surfaces
in Lipschitz domains locally modelled on convex polyhedra. We show that if such
a minimal surface is sufficiently close to an appropriate free-boundary plane,
then the surface is $C^{1,\alpha}$ graphical over this plane. We apply our
theorem to prove partial regularity results for free-boundary minimizing
hypersurfaces, and relative isoperimetric regions.

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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: econ
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex