The purpose of this paper is twofold. We first solve the Dirichlet problem for \(\tau \)-Hermitian–Einstein equations on holomorphic filtrations over compact Hermitian manifolds. Secondly, by using Uhlenbeck–Yau’s continuity method, we prove the existence of approximate \(\tau \)-Hermitian–Einstein structure on holomorphic filtrations over closed Gauduchon manifolds.

中文翻译：

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紧凑厄米流形上全纯过滤的标准度量

本文的目的是双重的。我们首先在紧致的Hermitian流形上的全纯过滤上解决\（\ tau \）- Hermitian-Einstein方程的Dirichlet问题。其次，通过使用Uhlenbeck-Yau的连续性方法，我们证明了封闭Gauduchon流形上全纯过滤上近似\（\ tau \）- Hermitian-Einstein结构的存在。