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arXiv · 1410.5252

Criteria for univalence and quasiconformal extension of harmonic mappings in terms of the Schwarzian DERIVATIVE

Rodrigo Hernández·María J. Martín
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Abstract

We prove that if the Schwarzian norm of a given complex-valued locally univalent harmonic mapping $f$ in the unit disk is small enough, then $f$ is, indeed, globally univalent and can be extended to a quasiconformal mapping in the extended complex plane.

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Rodrigo Hernández, María J. Martín. 2014-10-20. Criteria for univalence and quasiconformal extension of harmonic mappings in terms of the Schwarzian DERIVATIVE. https://arxiv.org/abs/1410.5252

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