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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnm152, 13 pages, doi:10.1093/imrn/rnm152 published on January 17, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

On Four-Dimensional Gradient Shrinking Solitons

Lei Ni and Nolan Wallach

Department of Mathematics, University of California at San Diego, La Jolla, CA 92093

Correspondence: Correspondence to be sent to: lni{at}math.ucsd.edu

In this paper, we classify the four-dimensional gradient shrinking solitons under certain curvature conditions satisfied by all solitons arising from finite-time singularities of Ricci flow on compact four-manifolds with positive isotropic curvature. As a corollary, we generalize a result of Perelman on three-dimensional gradient shrinking solitons to dimension four.



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This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
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Right arrow How to cite this article
Google Scholar
Right arrow Articles by Ni, L.
Right arrow Articles by Wallach, N.
Right arrow Search for Related Content
Social Bookmarking
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What's this?