Conformal weldings in the Loewner equation and Weil--Petersson quasislit-disks

Fei Tao, Huaying Wei, Yaosong Yang

A simple arc $\Gamma =\gamma (0,T]$, growing into the unit disk $\mathbb{D}$ from its boundary, generates a driving term $\xi$ and a conformal welding $\varphi$ through the Loewner differential equat…