Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Coarea Inequality   The aim of this paper is to provide a self-contained proof of a general case
of the coarea inequality, also known as the Eilenberg inequality. The result is
known, but we are not aware of any place that a proof would be written with all
details. The known proof is based on a difficult result of Davies. Our proof is
elementary and does not use Davies' theorem. Instead we use an elegant argument
that we learned from Nazarov through MathOverflow. We also obtain some
generalizations of the coarea inequality.

36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org