Complex geodesics in tube domains and their role in the study of harmonic mappings in the disc (Q2151144)

In this paper, the author continues the research from the work of \textit{P. Pflug} and \textit{W. Zwonek} [Forum Math. 30, No. 1, 159--170 (2018; Zbl 1384.32012)] on the structure of complex geodesics in tube domains over (bounded) convex bases. These results let understand better how complex geodesics in tube domains look like. In some special cases a more explicit form of the geodesics than the existing ones are provided. As one of the consequences of the study an effective formula for the Kobayashi-Royden metric in the tube domain \(T_{{\mathbb{B}}_n}\) at the origin is given. The results on the Kobayashi-Royden metric in a natural way provide versions of the Schwarz Lemma for harmonic mappings. A result that could be described as a refinement of the Radó-Kneser-Choquet Theorem with the homeomorphisms on the boundary replaced by bivalent functions onto a proper subset of the boundary of the convex domain is presented.