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

Robert J. Berman, Tamás Darvas, Chinh H. Lu

Let $(X,\omega )$ be a compact connected Kähler manifold and denote by $({\mathcal{E}}^p,d_p)$ the metric completion of the space of Kähler potentials ${\mathcal{H}}_{\omega }$ with respect to the $L^…