Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rank-one convexity implies polyconvexity in isotropic planar
  incompressible elasticity   We study convexity properties of energy functions in plane nonlinear
elasticity of incompressible materials and show that rank-one convexity of an
objective and isotropic elastic energy $W$ on the special linear group
$\mathrm{SL}(2)$ implies the polyconvexity of $W$.

3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph