📝 SummarXiv

Abstract

Given a compact K\"ahler manifold, we provide a uniform YTD correspondence that characterizes the existence of a unique constant scalar curvature metric using ample/K\"ahler test configurations. The main point of our approach is to replace the $K$ energy with much better behaving variants, whose properties are similar to the Ding energy from the Fano case. Connections with the non-Archimedean point of view on K-stability are also briefly discussed.