Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasiconformal harmonic mappings between two doubly connected domains in
  the plane   It is known for some time that there exists an energy-minimal diffeomorphism
between two doubly-connected domains $\Omega$ and $D$ provided that
$\mathrm{Mod}(\Omega)\le \mathrm{Mod}{D}$ and that diffeomorphism is harmonic
\cite{tedi}. In this note we give a short proof of the fact that for given
annuli $\Omega$ and $D$ satisfying the condition $\mathrm{Mod}(\Omega)\le
\mathrm{Mod}(D)$ there exist a $K-$quasiconformal harmonic diffeomorphism
$f:\Omega\onto D$, where $K=K(\tau)$, $\tau=\mathrm{Mod}(\Omega)/
\mathrm{Mod}(D)$ and $\lim_{\tau\to 1}K(\tau)=1$.

15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
18
The categories of this paper are: econ