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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Short-time existence of the Ricci flow on noncompact Riemannian manifolds


Author: Guoyi Xu
Journal: Trans. Amer. Math. Soc. 365 (2013), 5605-5654
MSC (2010): Primary 35K45, 53C44
Published electronically: June 28, 2013
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Abstract: In this paper, we give the first detailed proof of the short-time existence of Deane Yang's local Ricci flow. Then, using the local Ricci flow, we prove the short-time existence of the Ricci flow on noncompact manifolds, whose Ricci curvature has global lower bound and sectional curvature has only local average integral bound. The short-time existence of the Ricci flow on noncompact manifolds with bounded curvature was studied by Wan-Xiong Shi in the 1990s. As a corollary of our main theorem, we obtain the short-time existence part of Shi's theorem in this more general context.


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Additional Information

Guoyi Xu
Affiliation: Department of Mathematics, University of California, Irvine, California 92617
Address at time of publication: Mathematical Sciences Center, Tsinghua University, Beijing, 100084, People’s Republic of China
Email: guoyixu@math.uci.edu, guoyi.xu@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05998-3
PII: S 0002-9947(2013)05998-3
Received by editor(s): December 28, 2010
Published electronically: June 28, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.