论文标题
CSCK问题中的大地射线和稳定性
Geodesic rays and stability in the cscK problem
论文作者
论文摘要
We prove that any finite energy geodesic ray with a finite Mabuchi slope is maximal in the sense of Berman-Boucksom-Jonsson, and reduce the proof of the uniform Yau-Tian-Donaldson conjecture for constant scalar curvature Kähler metrics to Boucksom-Jonsson's regularization conjecture about the convergence of non-Archimedean entropy functional.作为进一步的应用，我们表明，模型过滤的统一K稳定性条件和$ \ Mathcal {J}^{k_x} $ - 稳定性都是CSCK指标存在的足够条件。第一个条件也被认为是必要的。我们的论点还为所有两极分化的复式歧管提供了YTD猜想的感谢您的YTD构造版本的不同证明。这里证明的另一个结果是，与测试配置相关的地理射线的mabuchi斜率等于非Archimedean mabuchi不变。
We prove that any finite energy geodesic ray with a finite Mabuchi slope is maximal in the sense of Berman-Boucksom-Jonsson, and reduce the proof of the uniform Yau-Tian-Donaldson conjecture for constant scalar curvature Kähler metrics to Boucksom-Jonsson's regularization conjecture about the convergence of non-Archimedean entropy functional. As further applications, we show that a uniform K-stability condition for model filtrations and the $\mathcal{J}^{K_X}$-stability are both sufficient conditions for the existence of cscK metrics. The first condition is also conjectured to be necessary. Our arguments also produce a different proof of the toric uniform version of YTD conjecture for all polarized toric manifolds. Another result proved here is that the Mabuchi slope of a geodesic ray associated to a test configuration is equal to the non-Archimedean Mabuchi invariant.
