2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67414This note computes the "renormalized volume" and a renormalizedGauss-Bonnet-Chern formula for the Euler characteristic ofasymptotically complex hyperbolic Einstein (in short: ACHE)4-manifolds.revised version ; reference to math.DG/0404455 addedDifferential Geometry53C55, 58J28A remark on renormalized volume and Euler characteristic for ACHE 4-manifoldstext