Solutions for the generalized Loewner differential equation in several complex variables (Q966434)

The authors study the general form of solutions to the Loewner differential equation which have the normalization \(f(z,t)=e^{tA}z+\dots\), where \(A\in L(\mathbb{C}^{n},\mathbb{C}^{n})\) has the property \(\max\left\{\Re \lambda:\lambda\in\sigma(A)\right\}<2\min\left\{\Re\left\langle A(z),z\right\rangle:\left\|z\right\|=1\right\}\). In particular, the form of the univalent solutions is obtained. The results are applied to subordination chains generated by spirallike mappings on the unit ball in \(\mathbb{C}^{n}\). The authors also determine the form of the solutions in the presence of certain coefficient bounds.