A preservation principle of extremal mappings near a strongly pseudoconvex point and its applications
Xiaojun Huang · Illinois Journal of Mathematics · 1994
XIAOJUN HUANG bottom tangent space must stay completely in the hole.In other words, we show that extremal mappings can only wind around the strongly pseudocon- vex boundary in the complex normal directions.As an application of this principle, we obtain the Lipschitz-1 continuity of a complex geodesic near a C3-strong pseudoconvex point.This improves, in some sense, a result in [Lml] and [Ab2], where only H61der-1/2 continuity was obtained for the complex geodesics of a Ca-strongly pseudoconvex domain.Another purpose of this paper is to study the boundary version of a uniqueness theorem for holomorphic self-mappings, by making use of iteration theory and the aforementioned regularity results of complex geodesics, especially the Lipschitzol continuity of an arbitrary holomorphic retract near a strongly pseudoconvex point.