Optimal asymptotic of the $J$ functional with respect to the $d_1$ metric

TL;DR

This paper establishes precise asymptotic inequalities for the $J$ functional relative to the $d_1$ metric on Kahler metrics, with applications to geodesic ray initial value problems.

Contribution

It provides sharp inequalities linking the $J$ functional and the $d_1$ metric, advancing understanding of their asymptotic relationship in Kahler geometry.

Findings

Sharp inequalities between $J$ functional and $d_1$ metric asymptotics

Applications to initial value problems for geodesic rays

Enhanced understanding of metric functionals in Kahler geometry

Abstract

We obtain sharp inequalities between the large scale asymptotic of the $J$ functional with respect to the $d_1$ metric on the space of Kahler metrics. Applications regarding the initial value problem for geodesic rays are presented.