English

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

Differential Geometry 2023-04-14 v1 Complex Variables

Abstract

In previous work, Darvas-George-Smith obtained inequalities between the large scale asymptotic of the JJ functional with respect to the d1d_1 metric on the space of toric K\"ahler metrics/rays. In this work we prove sharpness of these inequalities on all toric K\"ahler manifolds, and study the extremizing potentials/rays. On general K\"ahler manifolds we show that existence of radial extremizers is equivalent with the existence of plurisupported currents, as introduced and studied by McCleerey.

Keywords

Cite

@article{arxiv.2304.06323,
  title  = {Extremizers of the $J$ functional with respect to the $d_1$ metric},
  author = {Sam Bachhuber and Aaron Benda and Benjamin Christophel and Tamás Darvas},
  journal= {arXiv preprint arXiv:2304.06323},
  year   = {2023}
}

Comments

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