A rigidity result for holomorphic quadratic differentials of finite norm in the unit disk

Abstract

AbstractLet be a holomorphic quadratic differential of finite norm in the unit disk . Let be equipped with the metric . In this paper, we prove that a geodesic‐preserving map of the unit disk into itself is affine. A map is called geodesic‐preserving if the image of each geodesic is a geodesic. We make no assumptions on the continuity of such a map.