Extremal metrics on toric manifolds and homogeneous toric bundles

TL;DR

This paper proves the Yau-Tian-Donaldson conjecture for toric manifolds and homogeneous toric bundles, establishing a key link between geometric stability and extremal metrics.

Contribution

It provides a proof of the conjecture in the context of toric geometry, extending the understanding of extremal metrics on these manifolds.

Findings

Confirmed the conjecture for toric manifolds

Extended results to homogeneous toric bundles

Strengthened the link between stability and extremal metrics

Abstract

In this paper, we prove the Yau-Tian-Donaldson conjecture of the filtration version for toric manifolds and homogeneous toric bundles.