Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Commentary on Teichm{\"u}ller's paper ``Vollst{\"a}ndige L{\"o}sung
  einer Extremalaufgabe der quasikonformen Abbildung'' (Complete solution of an
  extremal problem of the quasiconformal mapping)   We comment on Teichm{\"u}ller 's paper ''Vollst{\"a}ndige L{\"o}sung einer
Extremalaufgabe der quasikonformen Abbildung'' (Complete solution of an
ex-tremal problem of the quasiconformal mapping),, published in 1941. In this
paper, Teichm{\"u}ller gives a proof of the existence of extremal
quasiconformal mappings in the case of the pentagon (disc with five
distinguished points on the boundary). The final version of this paper will
appear as a chapter in Volume VI of the Handbook of Teichm{\"u}ller theory.

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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con