Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Euclidean balls solve some isoperimetric problems with nonradial weights   In this note we present the solution of some isoperimetric problems in open
convex cones of $\R^n$ in which perimeter and volume are measured with respect
to certain nonradial weights. Surprisingly, Euclidean balls centered at the
origin (intersected with the convex cone) minimize the isoperimetric quotient.
Our result applies to all nonnegative homogeneous weights satisfying a
concavity condition in the cone. When the weight is constant, the result was
established by Lions and Pacella in 1990.

3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat