2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155056We observe inequalities involving the Herzlich volume of a 4-dimensional asymptotically complex hyperbolic Einstein manifold and its Euler characteristic provided the metrics is either Kaehler or selfdual. In the selfdual case we have to assume furthermore that the Kronheimer-Mrowka invariant is non vanishing.4 pages, no figureDifferential Geometry32Q20; 53C25text