Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compact stable hypersurfaces with free boundary in convex solid cones
  with homogeneous densities   We consider a smooth Euclidean solid cone endowed with a smooth homogeneous
density function used to weight Euclidean volume and hypersurface area. By
assuming convexity of the cone and a curvature-dimension condition we prove
that the unique compact, orientable, second order minima of the weighted area
under variations preserving the weighted volume and with free boundary in the
boundary of the cone are intersections with the cone of round spheres centered
at the vertex.

18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat