2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78637The Willmore conjecture states that any immersion F:T^2 -> R^n of a 2-torus into flat euclidean space satisfies $\int_{T^2} H^2\geq 2π^2$. We prove it under the condition that the L^p-norm of the Gaussian curvature is sufficiently small.26 pages, Latex2e, 3 figures using pstricks, some minor changes, numbers of theorems and propositions changedDifferential Geometry53A05 (Primary) 53A30, 58G30 (Secondary)text