Short-time existence of the Ricci flow on noncompact Riemannian manifolds
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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.References
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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
- Received by editor(s): December 28, 2010
- Published electronically: June 28, 2013
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 5605-5654
- MSC (2010): Primary 35K45, 53C44
- DOI: https://doi.org/10.1090/S0002-9947-2013-05998-3
- MathSciNet review: 3091259