Extremizers of the $J$ functional with respect to the $d_1$ metric

Abstract

In previous work, Darvas-George-Smith obtained inequalities between the large scale asymptotic of the $J$ functional with respect to the $d_1$ metric on the space of toric Kähler metrics/rays. In this work we prove sharpness of these inequalities on all toric Kähler manifolds, and study the extremizing potentials/rays. On general Kähler manifolds we show that existence of radial extremizers is equivalent with the existence of plurisupported currents, as introduced and studied by McCleerey.

Results from an REU project. arXiv admin note: text overlap with arXiv:2101.02589