Distortion Theory of Biunivalent Holomorphic Functions

Biunivalent holomorphic functions form an interesting class in geometric function theory and are associated with special functions and solutions of complex differential equations. This paper provides a complete distortion theory for such functions, in particular, the sharp coefficient estimates. Another interesting feature is that (in contrast to general collections of univalent functions) one obtains in the same fashion the sharp bounds for coefficients of biunivalent functions with k-quasiconformal extension for any k<1.