A uniform version of the Yau-Tian-Donaldson correspondence for extremal K\"ahler metrics on polarized toric manifolds

TL;DR

This paper addresses a uniform version of the Yau-Tian-Donaldson conjecture specifically for polarized toric manifolds, providing new insights into the stability and existence of extremal Kähler metrics.

Contribution

It introduces a uniform approach to the Yau-Tian-Donaldson conjecture and establishes a combinatorial criterion for uniform relative K-polystability.

Findings

Proves a uniform version of the Yau-Tian-Donaldson conjecture for polarized toric manifolds

Provides a combinatorial sufficient condition for uniform relative K-polystability

Advances understanding of stability conditions related to extremal Kähler metrics

Abstract

The aim of this paper is to solve a uniform version of the Yau-Tian-Donaldson conjecture for polarized toric manifolds. Also, we show a combinatorial sufficient condition for uniform relative K-polystability.