A quantization proof of the uniform Yau-Tian-Donaldson conjecture

Abstract

Using quantization techniques, we show that the $\delta$-invariant of Fujita-Odaka coincides with the optimal exponent in certain Moser-Trudinger type inequality. Consequently we obtain a uniform Yau-Tian-Donaldson theorem for the existence of twisted Kähler-Einstein metrics with arbitrary polarizations. Our approach mainly uses pluripotential theory, which does not involve Cheeger-Colding-Tian theory or the non-Archimedean language. A new computable criterion for the existence of constant scalar curvature Kähler metrics is also given.

v3, accepted version

References in corpus (4)

• Geodesic rays and stability in the cscK problem
• Basis divisors and balanced metrics
• Continuity of delta invariants and twisted Kähler--Einstein metrics
• K-stability of Fano varieties via admissible flags

Cited by in corpus (2)

• On K-stability of Calabi-Yau fibrations
• On boundedness and moduli spaces of K-stable Calabi-Yau fibrations over curves