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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The consistency and convergence of K-energy minimizing movements


Author: Jeffrey Streets
Journal: Trans. Amer. Math. Soc. 368 (2016), 5075-5091
MSC (2010): Primary 53C44
DOI: https://doi.org/10.1090/tran/6508
Published electronically: September 15, 2015
MathSciNet review: 3456172
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Abstract: We show that $ K$-energy minimizing movements agree with smooth solutions to Calabi flow as long as the latter exist. As corollaries we conclude that in a general Kähler class long time solutions of Calabi flow minimize both $ K$-energy and Calabi energy. Lastly, by applying convergence results from the theory of minimizing movements, these results imply that long time solutions to Calabi flow converge in the weak distance topology to minimizers of the $ K$-energy functional on the metric completion of the space of Kähler metrics, assuming one exists.


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Additional Information

Jeffrey Streets
Affiliation: Department of Mathematics, Rowland Hall, University of California, Irvine, Irvine, California 92617
Email: jstreets@uci.edu

DOI: https://doi.org/10.1090/tran/6508
Received by editor(s): February 17, 2014
Received by editor(s) in revised form: June 11, 2014, and June 22, 2014
Published electronically: September 15, 2015
Article copyright: © Copyright 2015 American Mathematical Society

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