The J-flow On Toric Manifolds

TL;DR

This paper investigates the J-flow on toric manifolds by analyzing the transition map between moment maps of two Kähler metrics, providing partial derivative bounds under Calabi symmetry.

Contribution

It introduces a new approach to studying the J-flow on toric manifolds via the transition map between moment maps, extending previous work under Calabi symmetry.

Findings

Partial bounds on derivatives of the transition map.

Extension of Fang-Lai's work to toric manifolds.

Insights into the structure of the J-flow in this setting.

Abstract

We study the J-flow on the toric manifolds, through study the transition map between the moment maps induced by two K\"{a}hler metrics, which is a diffeomorphism between polytopes. This is similar to the work of Fang-Lai, under the assumption of Calabi symmetry, they study the monotone map between two intervals. We get a partial bound of the derivatives of transition map.