Variational and non-Archimedean aspects of the Yau--Tian--Donaldson conjecture

TL;DR

This paper surveys recent advances connecting constant scalar curvature Kähler metrics with K-stability, emphasizing pluripotential theory and non-Archimedean geometry to deepen understanding of the Yau-Tian-Donaldson conjecture.

Contribution

It highlights the integration of pluripotential theory and non-Archimedean geometry into the study of K-stability and the Yau-Tian-Donaldson conjecture.

Findings

K-stability can be interpreted via non-Archimedean geometry

Pluripotential theory provides new tools for analyzing Kähler metrics

Recent developments support the conjecture's validity in broader contexts

Abstract

We survey some recent developments in the direction of the Yau-Tian-Donaldson conjecture, which relates the existence of constant scalar curvature K\"ahler metrics to the algebro-geometric notion of K-stability. The emphasis is put on the use of pluripotential theory and the interpretation of K-stability in terms of non-Archimedean geometry.