2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128580In this paper we prove novel lower bounds for the Ginzburg-Landau energy with or without magnetic field. These bounds rely on an improvement of the "vortex balls construction" estimates by extracting a new positive term in the energy lower bounds. This extra term can be conveniently estimated through a Lorentz space norm, on which it thus provides an upper bound. The Lorentz space $L^{2,\infty}$ we use is critical with respect to the expected vortex profiles and can serve to estimate the total number of vortices and get improved convergence results.52 pages, 1 figureAnalysis of PDEsMathematical Physics35J50, 58E50, 82D55text