Canonical Metrics on Holomorphic Filtrations over Compact Hermitian Manifolds

Abstract

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.

Keywords

$\tau $-Hermitian–Einstein equation')">$\tau $-Hermitian–Einstein equation / $\tau $-Hermitian–Einstein structure')">Approximate $\tau $-Hermitian–Einstein structure / Semi-stability / Holomorphic filtration / Gauduchon manifold

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