The consistency and convergence of K-energy minimizing movements
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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.References
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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
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 5075-5091
- MSC (2010): Primary 53C44
- DOI: https://doi.org/10.1090/tran/6508
- MathSciNet review: 3456172