Minimization of Arakelov K-energy for many cases

Source abstract

We prove that for various polarized varieties over Q‾, which broadly includes K-trivial case, K-ample case, Fano case, minimal models, and certain classes of fibrations, certain metrized “minimal-like” models minimize the Arakelov theoretic analog of the Mabuchi K-energy, as conjectured by the second author. This is an Arakelov theoretic analog of a result by the first author.