Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Nitsche conjecture   The conjecture in question concerns the existence of a harmonic homeomorphism
between circular annuli A(r,R) and A(r*,R*), and is motivated in part by the
existence problem for doubly-connected minimal surfaces with prescribed
boundary. In 1962 J.C.C. Nitsche observed that the image annulus cannot be too
thin, but it can be arbitrarily thick (even a punctured disk). Then he
conjectured that for such a mapping to exist we must have the following
inequality, now known as the Nitsche bound: R*/r* is greater than or equal to
(R/r+r/R)/2. In this paper we give an affirmative answer to his conjecture. As
a corollary, we find that among all minimal graphs over given annulus the upper
slab of catenoid has the greatest conformal modulus.

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The categories of this paper are: patt-sol
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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: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc