2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163634We prove that the canonical volume $K^3\geq {1/30}$ for all projective 3-folds of general type with $χ(\mathcal{O})\leq 0$. This bound is sharp.16 pages, Updated version, To appear in Journal of LMSAlgebraic GeometryThe canonical volume of threefolds of general type with $χ<1$text