摘要：

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