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

Fei Tao, Huaying Wei, Yaosong Yang

A simple arc $\hat{I}“={\hat{I}}^3(0,T]$, growing into the unit disk $\mathbb{D}$ from its boundary, generates a driving term $\hat{I}¾$ and a conformal welding $\ddot{I}•$ through the Loewner differential e…