On a classification of gradient shrinking solitons

The main purpose of this article is to provide an alternate proof to a result of Perelman on gradient shrinking solitons. Moreover in dimension three our proof generalizes Perelman's result by removing the -non-collapsing assumption and allowing general curvature growth. The method also allows us to prove a classification result on gradient shrinking solitons with vanishing Weyl curvature tensor in high dimensions, which includes the rotationally symmetric ones.