English

On a classification of the gradient shrinking solitons

Differential Geometry 2007-10-18 v1 Analysis of PDEs

Abstract

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 κ\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

Cite

@article{arxiv.0710.3194,
  title  = {On a classification of the gradient shrinking solitons},
  author = {Lei Ni and Nolan Wallach},
  journal= {arXiv preprint arXiv:0710.3194},
  year   = {2007}
}
R2 v1 2026-06-21T09:32:50.919Z