Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on the Hayman-Wu theorem   The Hayman-Wu theorem states that the preimage of a line or circle L under a
conformal mapping from the unit disc to a simply-connected domain U has total
Euclidean length bounded by an absolute constant. The best possible constant is
known to lie in the interval [pi^2, 4 pi), thanks to work of {\O}yma and Rohde.
Earlier, Brown Flinn showed that the total length is at most pi^2 in the
special case in which U contains L. Let r be the anti-M\"obius map that fixes L
pointwise. In this note we extend the sharp bound pi^2 to the case where each
connected component of the intersection of U with r(U) is bounded by one arc of
U and its image under r. We also strengthen the bounds slightly by replacing
Euclidean length with the strictly larger spherical length restricted to the
unit disc.

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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-th