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Kähler-Ricci flow with degenerate initial class


Author: Zhou Zhang
Journal: Trans. Amer. Math. Soc. 366 (2014), 3389-3403
MSC (2010): Primary 53C44; Secondary 14E30, 58J35
DOI: https://doi.org/10.1090/S0002-9947-2014-05943-6
Published electronically: March 13, 2014
MathSciNet review: 3192600
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Abstract: In an earlier joint work with X. X. Chen and G. Tian (2011), we introduced the weak Kähler-Ricci flow for various geometric motivations. In this current work, we give further consideration to setting up the weak flow by allowing the initial class to be not necessarily Kähler. It's shown that the construction is compatible with the earlier construction in the Kähler case. We also discuss the convergence as $ t\to 0^+$, which is of great interest in this topic, and provide related motivation.


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Additional Information

Zhou Zhang
Affiliation: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia
Email: zhangou@maths.usyd.edu.au

DOI: https://doi.org/10.1090/S0002-9947-2014-05943-6
Keywords: Geometric evolution equation, minimal model program
Received by editor(s): January 6, 2012
Published electronically: March 13, 2014
Additional Notes: The author was supported in part by NSF 0904760 and ARC Discovery Project DP110102654.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.