6 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 …
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 Kähle…
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: where…
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 curvatu…
RC-positivity, Schwarz's lemma and comparison theorems
Zhiyao Xiong, Xiaokui Yang, Shing-Tung Yau
It is well-known that the classical Schwarz lemma yields an explicit comparison of two Hermitian metrics with uniform constant negative curvature bounds through holomorphic maps be…
Conjugate radius, volume comparison and rigidity
Zhiyao Xiong, Xiaokui Yang
In this paper, we prove conjugate radius estimate, volume comparison and rigidity theorems for Kähler manifolds with various curvature conditions.