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arXiv · 2304.06323

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

Sam Bachhuber·Aaron Benda·Benjamin Christophel·Tamás Darvas
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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 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.

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Sam Bachhuber, Aaron Benda, Benjamin Christophel, Tamás Darvas. 2023-04-13. Extremizers of the $J$ functional with respect to the $d_1$ metric. https://arxiv.org/abs/2304.06323

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