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On the convergence of the Calabi flow


Author: Weiyong He
Journal: Proc. Amer. Math. Soc. 143 (2015), 1273-1281
MSC (2010): Primary 53C55; Secondary 35K55
DOI: https://doi.org/10.1090/S0002-9939-2014-12318-5
Published electronically: November 4, 2014
MathSciNet review: 3293741
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Abstract: Let $ (M, [\omega _0], J)$ be a compact Kähler manifold without holomorphic vector field. Suppose $ \omega _0$ is (the unique) constant scalar curvature metric. We show that the Calabi flow with any smooth initial metric converges to the constant scalar curvature metric $ \omega _0$ with the assumption that Ricci curvature stays uniformly bounded.


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Additional Information

Weiyong He
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
Email: whe@uoregon.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-12318-5
Received by editor(s): June 17, 2013
Received by editor(s) in revised form: July 19, 2013
Published electronically: November 4, 2014
Communicated by: Lei Ni
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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