The consistency and convergence of K-energy minimizing movements

Streets, Jeffrey

doi:10.1090/tran/6508

The consistency and convergence of K-energy minimizing movements
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by Jeffrey Streets PDF

Trans. Amer. Math. Soc. 368 (2016), 5075-5091 Request permission

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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