2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/140190The main purpose of this article is to provide an alternate proof to a result of Perelman on gradient shrinking solitons. In dimension three we also generalize the result by removing the $κ$-non-collapsing assumption. In high dimension this new method allows us to prove a classification result on gradient shrinking solitons with vanishing Weyl curvature tensor, which includes the rotationally symmetric ones.Differential GeometryAnalysis of PDEstext