@article{a2fa0d00b6484f54972a090dd0ae42e1,
title = "Pre-Schwarzian and Schwarzian Derivatives of Harmonic Mappings",
abstract = "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 ωf of f. Using the new definition for the Schwarzian derivative of harmonic mappings, we prove theorems analogous to those by Chuaqui, Duren, and Osgood. Also, we obtain a Becker-type criterion for the univalence of harmonic mappings.",
keywords = "Becker{\textquoteright}s criterion, Convexity, Harmonic mappings, Pre-Schwarzian derivative, Schwarzian derivative, Univalence",
author = "Rodrigo Hern{\'a}ndez and Mart{\'i}n, {Mar{\'i}a J.}",
note = "Funding Information: The authors were partially supported by Fondecyt Grant # 1110160, Chile, and Grants MTM2009-14694-C02-01 (MICINN) and MTM2012-37436-C02-02 (MINECO), Spain. Publisher Copyright: {\textcopyright} 2013, Mathematica Josephina, Inc.",
year = "2013",
month = jan,
doi = "10.1007/s12220-013-9413-x",
language = "English",
volume = "25",
pages = "64--91",
journal = "Journal of Geometric Analysis",
issn = "1050-6926",
publisher = "Springer New York",
number = "1",
}