2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56813We prove the conjecture that a monopole in three-dimensional anti-de Sitter space can be completely determined by its ``holographic'' image on the conformal boundary two-sphere.18 pages. Complete revision of the paper, focusing on clearer exposition. Although sometimes stated differently, the results remain the same as in the original versionMathematical PhysicsHigh Energy Physics - TheoryDifferential Geometry81T13; 53C07text