Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the relationship between rank-$(n-1)$ convexity and ${\mathcal
  S}$-quasiconvexity   We prove that rank-$(n-1)$ convexity does not imply ${\mathcal
S}$-quasiconvexity (i.e., quasiconvexity with respect to divergence free
fields) in ${\mathbb M}^{m\times n}$ for $m>n$, by adapting the well-known
Sverak's counterexample [5] to the solenoidal setting. On the other hand, we
also remark that rank-$(n-1)$ convexity and ${\mathcal S}$-quasiconvexity turn
out to be equivalent in the space of $n\times n$ diagonal matrices. This
follows by a generalization of Mueller's work [4].

28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an