Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stretching and Rotation of Planar Quasiconformal Mappings on a Line   In this article, we examine stretching and rotation of planar quasiconformal
mappings on a line. We show that for almost every point on the line, the set of
complex stretching exponents (describing stretching and rotation jointly) is
contained in the disk $ \overline{B}(1/(1-k^4),k^2/(1-k^4))$. This yields a
quadratic improvement over the known optimal estimate for general sets of
Hausdorff dimension $1$. Our proof is based on holomorphic motions and
estimates for dimensions of quasicircles. We also give a lower bound for the
dimension of the image of a $1$-dimensional subset of a line under a
quasiconformal mapping.

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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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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: cs