Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On The Existence of Min-Max Minimal Surface of Genus $g\geq 2$   In this paper, we build up a min-max theory for minimal surfaces using
sweepouts of surfaces of genus $g\geq 2$. We develop a direct variational
methods similar to the proof of the famous Plateau problem by J. Douglas and T.
Rado. As a result, we show that the min-max value for the area functional can
be achieved by a bubble tree limit consisting of branched genus-$g$ minimal
surfaces with nodes, and possibly finitely many branched minimal spheres. We
also prove a Colding-Minicozzi type strong convergence theorem similar to the
classical mountain pass lemma. Our results extend the min-max theory developed
by Colding-Minicozzi and the author to all genera.

27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: stat
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg