A quantization proof of the uniform Yau–Tian–Donaldson conjecture
Kewei Zhang
Beijing Normal University, China
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Abstract
Using quantization techniques, we show that the -invariant of Fujita–Odaka coincides with the optimal exponent in a 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.
Cite this article
Kewei Zhang, A quantization proof of the uniform Yau–Tian–Donaldson conjecture. J. Eur. Math. Soc. (2023), published online first
DOI 10.4171/JEMS/1373