Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Min-max theory for free boundary minimal hypersurfaces I - regularity
  theory   In 1960s, Almgren initiated a program to find minimal hypersurfaces in
compact manifolds using min-max method. This program was largely advanced by
Pitts and Schoen-Simon in 1980s when the manifold has no boundary. In this
paper, we finish this program for general compact manifold with nonempty
boundary. As a result, we prove the existence of a smooth embedded minimal
hypersurface with free boundary in any compact smooth Euclidean domain. An
application of our general existence result combined with the work of Marques
and Neves shows that for any compact Riemannian manifolds with nonnegative
Ricci curvature and convex boundary, there exist infinitely many embedded
minimal hypersurfaces with free boundary which are properly embedded.

20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg