Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rank-one convexity implies quasiconvexity for two-component maps   We prove that, for two-component maps, rank-one convexity is equivalent to
quasiconvexity. The essential tool for the proof is a fixed-point argument for
a suitable set-valued map going from one component to the other and preserving
decomposition directions in the $(H_n)$-condition formalism; the existence of a
fixed point ensures that, in addition to keeping decomposition directions,
joint volume fractions are preserved as well. When maps have more than two
components, then fixed points exist for every combination of two components,
but they do not match in general.

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The categories of this paper are: hep-ph
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org