2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166658We concerns here with the continuity on the geometry of the second Riemannian L^p-Sobolev best constant B_0(p,g) associated to the AB program. Precisely, for 1 <= p <= 2, we prove that B_0(p,g) depends continuously on g in the C^2-topology. Moreover, this topology is sharp for p = 2. From this discussion, we deduce some existence and C^0-compactness results on extremal functions.19 pagesDifferential GeometryAnalysis of PDEs32Q10, 53C21text