Mathematical Research Letters

Volume 15 (2008)

Number 5

On a classification of gradient shrinking solitons

Pages: 941 – 955

DOI: http://dx.doi.org/10.4310/MRL.2008.v15.n5.a9

Authors

Lei Ni (University of California at San Diego)

Nolan Wallach (University of California at San Diego)

Abstract

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 $\kappa$-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.

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