2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/205049We extend the validity of Dain's angular-momentum inequality to maximal, asymptotically flat, initial data sets on a simply connected manifold with several asymptotically flat ends which are invariant under a U(1) action and which admit a twist potential.added Appendix C on uniquenessGeneral Relativity and Quantum CosmologyMass and angular-momentum inequalities for axi-symmetric initial data sets. II. Angular-momentumtext