7 papers
Iterative construction of Hermitian-Einstein metrics on stable bundles
Jiaxuan Fan, Zhiyao Xiong, Xiaokui Yang +1
Let be a stable holomorphic vector bundle over a compact Kähler (or Gauduchon) manifold . We show that for any real number and any initial Hermitian metric $h…
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 be a holomorphic vector bundle over a compact Kähl…
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…
Existence of Hermitian metrics with prescribed Hermitian-Yang-Mills tensors II
Jiaxuan Fan, Mingwei Wang, Xiaokui Yang +1
In this paper, we solve the prescribed Hermitian-Yang-Mills tensor problem for Higgs bundles over compact complex manifolds. Let be a Higgs bundle over a compact Hermiti…
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 be a holomorphic vector bundle over a compact Kähler manifold . Suppose that there…
Laplacian comparison theorems on complete Kähler manifolds and applications
Jiaxuan Fang, Zhiyao Xiong, Xiaokui Yang
In this paper, we establish new Laplacian comparison theorems and rigidity theorems for complete Kähler manifolds under new curvature notions that interpolate between Ricci curvat…