2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98110Following Riemann's idea, we prove the existence of a minimal disk in Euclidean space bounded by three lines in generic position and with three helicoidal ends of angles less than $π$. In the case of general angles, we prove that there exist at most four such minimal disks, we give a sufficient condition of existence in terms of a system of three equations of degree 2, and we give explicit formulas for the Weierstrass data in terms of hypergeometric functions. Finally, we construct constant-mean-curvature-one trinoids in hyperbolic space by the method of the conjugate cousin immersion.33 pages, 8 figuresDifferential Geometry53A10; 53C42; 53A35; 30F45text