Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Weakly Einstein critical metrics of the volume functional on compact
  manifolds with boundary
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat