Mihai Iancu
Babeş-Bolyai University, Cluj-Napoca, Romania

We consider biholomorphic mappings on the Euclidean unit ball $\mathbb{B}^n$ which embed into normal Loewner chains whose differential at the origin satisfies a first-order homogeneous linear differential equation for a time-dependent linear operator. More precisely, we discuss the dependence of $\widetilde{S}^T_A(\mathbb{B}^n)$ with respect to $A$ and $T$, where $\widetilde{S}^T_A(\mathbb{B}^n)$ is a compact family of mappings that have generalized parametric representation on $\mathbb{B}^n$ given by $A:[0,\infty)\to L(\mathbb{C}^n)$ and starting at $T\in[0,\infty)$. Joint work with Hidetaka Hamada (Kyushu Sangyo University, Fukuoka, Japan) and Gabriela Kohr (Babeş-Bolyai University, Cluj-Napoca, Romania).