## On a classification of the gradient shrinking solitons

Ni, Lei
Wallach, Nolan
##### Description
The 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 $\kappa$-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.
##### Keywords
Mathematics - Differential Geometry, Mathematics - Analysis of PDEs