Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Co-Dimension One Area-Minimizing Currents with $C^{1,\alpha}$
  Tangentially Immersed Boundary   We introduce and study co-dimension one area-minimizing locally rectifiable
currents $T$ with $C^{1,\alpha}$ tangentially immersed boundary: $\partial T$
is locally a finite sum of orientable co-dimension two submanifolds which only
intersect tangentially with equal orientation. We show that any such $T$ is
supported in a smooth hypersurface near any point on the support of $\partial
T$ where $T$ has tangent cone which is a hyperplane with constant orientation
but non-constant multiplicity. We also introduce and study co-dimensional one
area-minimizing locally rectifiable currents $T$ with boundary having
co-oriented mean curvature: $\partial T$ has generalized mean curvature
$H_{\partial T} = h \nu_{T}$ with $h$ a real-valued function and $\nu_{T}$ the
generalized outward pointing unit normal of $\partial T$ with respect to $T.$

25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: eess
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
6
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: adap-org