Abstract:We give a variational proof of a version of the Yau–Tian–Donaldson conjecture for twisted Kähler–Einstein currents, and use this to express the greatest (twisted) Ricci lower bound in terms of a purely algebro-geometric stability threshold. Our approach does not involve a continuity method or the Cheeger–Colding–Tian theory, and uses instead pluripotential theory and valuations. Along the way, we study the relationship between geodesic rays and non-Archimedean metrics.

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中文翻译：

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Yau-Tian-Donaldson 猜想的变分方法

摘要：我们对扭曲的 Kähler-Einstein 电流的 Yau-Tian-Donaldson 猜想的一个版本给出了变分证明，并用它来表达最大（扭曲的）Ricci 下界纯粹代数几何稳定性阈值。我们的方法不涉及连续性方法或 Cheeger-Colding-Tian 理论，而是使用多势理论和估值。在此过程中，我们研究了测地线与非阿基米德度量之间的关系。

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