Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiplicity one for min-max theory in compact manifolds with boundary
  and its applications   We prove the multiplicity one theorem for min-max free boundary minimal
hypersurfaces in compact manifolds with boundary of dimension between 3 and 7
for generic metrics. To approach this, we develop existence and regularity
theory for free boundary hypersurface with prescribed mean curvature, which
includes the regularity theory for minimizers, compactness theory, and a
generic min-max theory with Morse index bounds. As applications, we construct
new free boundary minimal hypersurfaces in the unit balls in Euclidean spaces
and self-shrinkers of the mean curvature flows with arbitrarily large entropy.

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The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph