# Convexity of the extended K-energy and the large time behavior of the weak Calabi flow

@inproceedings{Berman2017ConvexityOT, title={Convexity of the extended K-energy and the large time behavior of the weak Calabi flow}, author={Robert J. Berman and Tam'as Darvas and Chinh H. Lu}, year={2017} }

- Published 2017
DOI:10.2140/gt.2017.21.2945

Let (X, omega) be a compact connected Kahler manifold and denote by (epsilon(p), d(p)) the metric completion of the space of Kahler potentials H-omega with respect to the L-p - type path length metric d(p). First, we show that the natural analytic extension of the (twisted) Mabuchi K-energy to epsilon(p) is a d(p)-lsc functional that is convex along finite-energy geodesics. Second, following the program of J Streets, we use this to study the asymptotics of the weak (twisted) Calabi flow inside… CONTINUE READING

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