Dynamics Seminar

David Pfrang

(Jacobs University)

"The value range of typically real bounded univalent functions"

Date: Tue, September 13, 2016
Time: 14:15
Place: Research I Seminar Room

Abstract: A function \(f\in\text{Hol}(\mathbb{D}, \mathbb{D})\) is called \(\textit{typically real}\), if \[ \text{Im } z=0~~~\Leftrightarrow~~~\text{Im } f(z)=0~~~\text{for all}~z\in\mathbb{D}. \] After giving a brief overview about the deterministic Loewner Differential Equation, I will explain how to specialize the general Loewner-Kufarev-ODE in order to obtain the exact value range \[ \{ f(z_0)~\vert~f\in\text{Hol}(\mathbb{D},\mathbb{D})~\text{is typically real and normalized by }f(0)=0,~f'(0)>0~\} \] for every \(z_0\in\mathbb{D}\).