On univalent solutions of the biharmonic equation

By Zayid Abdulhadi, Y. Abu Muhanna, Suheil A. Khuri. 2005

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We analyze the univalence of the solutions of the biharmonic equation. In particular, we show that if is a biharmonic map in the form,, where is harmonic, then is starlike whenever is starlike. In addition, when,, where and are harmonic, we show that is locally univalent whenever is starlike and is orientation preserving.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d7322e8682267567c39966f149dc9a623df647cd