Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tensorization of Cheeger energies, the space $H^{1,1}$ and the area
  formula for graphs   First we study in detail the tensorization properties of weak gradients in
metric measure spaces $(X,d,m)$. Then, we compare potentially different notions
of Sobolev space $H^{1,1}(X,d,m)$ and of weak gradient with exponent 1.
Eventually we apply these results to compare the area functional
$\int\sqrt{1+|\nabla f|_w^2}\,dm$ with the perimeter of the subgraph of $f$, in
the same spirit as the classical theory.

7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int