Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A simple example of the weak discontinuity of $f\mapsto \int \det \nabla
  f$   In this short note I construct a sequence of conformal diffeomorphisms $f_n$
from the $d$-dimensional unit ball to itself that converges weakly to a
constant in $W^{1,d}$. This is a simpler example than the ones that commonly
appear in the literature for the discontinuity of the functional $f\mapsto \int
\det \nabla f$ in the weak $W^{1,d}$-topology, and shows that this
discontinuity is not due to shear or failure of injectivity. It is also a
minimizing sequence of the $W^{1,d}$ norm among functions of a given volume of
the image.

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The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin