Complex geodesics and iterates of holomorphic maps on convex domains in $\textbf {C}^ n$

Abstract:

We study complex geodesics $f:\Delta \to \Omega$, where $\Delta$ is the unit disk in ${\mathbf {C}}$ and $\Omega$ belongs to a class of bounded convex domains in ${{\mathbf {C}}^n}$ with no boundary regularity assumption. Along with continuity up to the boundary, existence of such complex geodesics with two prescribed values $z$, $w \in \bar \Omega$ is established. As a consequence we obtain some new results from iteration theory of holomorphic self maps of bounded convex domains in ${{\mathbf {C}}^n}$.