Journal of Inequalities and Applications 
Volume 2005 (2005), Issue 5, Pages 469-478
doi:10.1155/JIA.2005.469

On univalent solutions of the biharmonic equation

Z. AbdulHadi, Y. Abu Muhanna, and S. Khuri

 Department of Mathematics, American University of Sharjah, P.O. Box 26666, Sharjah, United Arab Emirates
Received 16 January 2004

Abstract

We analyze the univalence of the solutions of the biharmonic equation. In particular, we show that if F is a biharmonic map in the form F(z)=r2G(z), |z|<1, where G is harmonic, then F is starlike whenever G is starlike. In addition, when F(z)=r2G(z)+K(z), |z|<1, where G and K are harmonic, we show that F is locally univalent whenever G is starlike and K is orientation preserving.