2 problems

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Uniform log Yau–Tian–Donaldson conjecture for cscK cone metrics
Uniform log Yau–Tian–Donaldson conjecture. The polarised pair $((X,L);D)$ admits a cscK cone metric if and only if it is uniformly log $K$ -stable.
Conjectureopencone-metrics kahler-geometry uniform-k-stabilityarXiv posted 2 days ago
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Existence of K-stable but not uniformly K-stable polarized normal varieties
A polarized normal variety is a pair $(X,L)$ consisting of a normal variety $X$ and a polarization $L$ . K-stability and uniform K-stability are the corresponding notions for polari…
Conjecturesolvedk-stability polarized-varieties uniform-k-stabilityarXiv posted 2 days ago

Uniform log Yau–Tian–Donaldson conjecture for cscK cone metrics