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

  • Kewei Zhang

    Beijing Normal University, China
A quantization proof of the uniform Yau–Tian–Donaldson conjecture cover
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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. 26 (2024), no. 12, pp. 4763–4778

DOI 10.4171/JEMS/1373