Complex Geodesics in Tube Domains and Their Role in the Study of Harmonic Mappings in the Disc

We continue the research on structure of complex geodesics in tube domains over (bounded) convex bases. In some special cases a more explicit form than existing ones are provided. As one consequences our study an effective formula for Kobayashi—Royden metric domain $${T_{{\mathbb{B}_n}}}$$ at origin is given. The results natural way provide versions Schwarz Lemma harmonic mappings. also present result mappings defined disc that may be seen as generalisation Radó—Kneser—Choquet Theorem class bivalent lets understand better geometry domains.