Abstract:In this paper, we introduce a broad class of flows, including the prescribed Hermitian-Yang-Mills flow:
$$\frac{\partial h}{\partial t}=-\Lambda_{\omega_g}\left(\sqrt R^h\right)+P$$
where $P\in\Gamma(M,E^*\otimes\bar{E}^*)$ is a prescribed Hermitian tensor associated with a holomorphic vector bundle $E$ over a Kähler (or Hermitian) manifold $(M,\omega_g)$. We establish the long-time convergence of the flow to a limiting metric $h_{\infty}$ and use it to solve the prescribed Hermitian-Yang-Mills tensor equation
$$\Lambda_{\omega_g}\left(\sqrt R^{h_\infty}\right)=P,
$$
for a general class of prescribed Hermitian tensors $P$.
The crucial uniform $C^0$-estimate of $\{h(t)\}$ along the flow is obtained via a parabolic comparison principle.
From: Xiaokui Yang [view email]
[v1]
Fri, 19 Jun 2026 03:21:33 UTC (31 KB)
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