Rough singular Kähler-Einstein metrics, when the metric completion is an RCD space, are equivalent to the Eyssidieux-Guedj-Zeriahi notion and imply log terminal singularities; this applies to tangent cones of noncollapsed Kähler limits.
On noncollapsed $\mathbb{F}$-limit metric solitons
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abstract
A noncollapsed $\mathbb{F}$-limit metric soliton is a self-similar singularity model that inevitably arises when studying the Ricci flow with the tool of $\mathbb{F}$-convergence [Bam20a,Bam20b,Bam20c]. In this article, we shall present a systematic study of the noncollapsed $\mathbb{F}$-limit metric soliton, and show that, apart from the known results in [Bam20c], it satisfies many properties of smooth Ricci shrinkers. In particular, we show a quadratic lower bound for the scalar curvature, a local gap theorem, a global Sobolev inequality, and an optimal volume growth lower bound.
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Remarks on Singular K\"ahler-Einstein Metrics
Rough singular Kähler-Einstein metrics, when the metric completion is an RCD space, are equivalent to the Eyssidieux-Guedj-Zeriahi notion and imply log terminal singularities; this applies to tangent cones of noncollapsed Kähler limits.