2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66647Through the study of some elliptic and parabolic fully nonlinear PDEs, we establish conformal versions of quermassintegral inequality, the Sobolev inequality and the Moser-Trudinger inequality for the geometric quantities associated to the Schouten tensor on locally conformally flat manifolds.30 pages. Final version, accepted by Duke Math. JDifferential Geometrytext