Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pre-Schwarzian and Schwarzian derivatives of harmonic mappings   In this paper we introduce a definition of the pre-Schwarzian and the
Schwarzian derivatives of any locally univalent harmonic mapping $f$ in the
complex plane without assuming any additional condition on the (second complex)
dilatation $\omega_f$ of $f$. Using the new definition for the Schwarzian
derivative of harmonic mappings, we prove analogous theorems to those by
Chuaqui, Duren, and Osgood. Also, we obtain a Becker-type criterion for the
univalence of harmonic mappings.

16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
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The categories of this paper are: econ
25
The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
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The categories of this paper are: eess
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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: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org