Boundary extensions of quasi-isometries on pseudoconvex domains

In this talk, by using the Gehring–Hayman-type theorem on some complex domains in $\mathbb C^n$, we will give some results on bi-Hölder extensions not only for biholomorphisms, but also for more general Kobayashi metric quasiisometries between these domains. At last, we show that the identity map for the smoothly bounded pseudoconvex domain of finite type in $\mathbb C^2$ extends to a bi-Hölder map between the Euclidean boundary and Gromov boundary.