S. Yau

works on

graph statistics 1 network analysis 1 non-euclidean data 1 systems biology 1 topological data analysis 1

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math.DG2026

Iterative construction of Hermitian-Einstein metrics on stable bundles

Jiaxuan Fan, Zhiyao Xiong, Xiaokui Yang +1

Let $E$ be a stable holomorphic vector bundle over a compact KÃ¤hler (or Gauduchon) manifold $(M, I ¨ _{g})$ . We show that for any real number $I^¼ > 0$ and any initial Hermitian metric $h…

math.DG2026

The prescribed Hermitian-Yang-Mills flow II

Zhiyao Xiong, Xiaokui Yang, Shing-Tung Yau

We prove an analogue of the classical Donaldson-Uhlenbeck-Yau theorem by using the prescribed Hermitian-Yang-Mills flow. Let $E$ be a holomorphic vector bundle over a compact KÃ¤hl…

math.DG2026

The prescribed Hermitian-Yang-Mills flow I

Zhiyao Xiong, Xaokui Yang, Shing-Tung Yau

In this paper, we introduce a broad class of flows, including the prescribed Hermitian-Yang-Mills flow: $\frac{\partial h}{\partial t} = - I^_{I ¨ _{g}} (R^{h}) + P$ where $…

math.DG2026

Existence of twisted Hermitian-Einstein metrics on unstable vector bundles

Mingwei Wang, Xiaokui Yang, Shing-Tung Yau

In this paper, we demonstrate that twisted Hermitian-Einstein metrics on holomorphic vector bundles exist without obstruction. More precisely, for an arbitrary holomorphic vector b…

math.DG2026

Existence of Hermitian metrics with prescribed Hermitian-Yang-Mills tensors I

Mingwei Wang, Xiaokui Yang, Shing-Tung Yau

In this paper, we solve the prescribed Hermitian-Yang-Mills tensor problem. Let $E$ be a holomorphic vector bundle over a compact KÃ¤hler manifold $(M, I ¨ _{g})$ . Suppose that there…