2 problems

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Mabuchi–Tian properness conjecture for constant scalar curvature Kähler metrics
Mabuchi–Tian conjecture. The Mabuchi K-energy functional is proper if and only if there exists a CSCK metric in the class $[\omega]$ .
Conjectureopencsck-metrics kahler-geometry mabuchi-energyarXiv posted 2 days ago
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The coercivity form of the Yau–Tian–Donaldson conjecture
Coercivity form of the Yau–Tian–Donaldson conjecture. The following are equivalent:
Conjectureopenkahler-geometry k-stability mabuchi-energyarXiv posted 2 days ago

Mabuchi–Tian properness conjecture for constant scalar curvature Kähler metrics