14 citations · 20 across the 15 of their papers we have counts for
16 papers
Mean curvature nonpositivity and rational connectedness
Chuanjing Zhang, Xi Zhang
Let be a compact Gauduchon manifold and let be a holomorphic vector bundle on . We establish equivalent conditions for the existence of a Hermitian metric on wit…
Long-time behavior of the Hermitian-Yang-Mills flow on non-Kähler manifolds
Zeng Chen, Chao Li, Chuanjing Zhang +1
In this paper, we study the long-time behavior of the Hermitian-Yang-Mills flow over compact Hermitian manifolds. We obtain the monotonicity of lower bound and upper bound of the e…
Non-abelian Hodge correspondence over singular Kähler spaces
Chuanjing Zhang, Shiyu Zhang, Xi Zhang
In this paper, we establish the non-abelian Hodge correspondence over compact Kähler spaces with Kawamata log terminal (klt) singularities as well as over their regular loci, there…
The Miyaoka-Yau inequality for minimal Kähler klt spaces
Chuanjing Zhang, Shiyu Zhang, Xi Zhang
Let be a compact Kähler space with quotient singularities in codimension . In terms of orbifold Chern classes, we prove a generalized Bogomolov-Gieseker inequality for a ref…
The finite time blow-up of the Yang-Mills flow
Wang Guan Xiang, Zhang Chuan Jing
In this paper, we shall prove that, on a non-flat Riemannian vector bundle over a compact Riemannian manifold, the smooth solution of the Yang-Mills flow will blow up in finite tim…
Mean curvature positivity and rational connectedness
Chao Li, Chuanjing Zhang, Xi Zhang
In this paper, we use Uhlenbeck-Yau's continuity method to establish the correspondence between the mean curvature positivity and the HN-positivity on holomorphic vector bundles ov…
Generalized Donaldson's functionals and related nonlinear partial differential equations
Chuanjing Zhang, Xi Zhang
In this paper, we introduce a family of generalized Donaldson's functional on holomorphic vector bundles, whose Euler-Lagrange equations are a vector bundle version of the complex…
Projectively flat bundles and semi-stable Higgs bundles
Changpeng Pan, Chuanjing Zhang, Xi Zhang
The Corlette-Donaldson-Hitchin-Simpson's correspondence states that, on a compact Kähler manifold , there is a one-to-one correspondence between the moduli space of semisim…
Flat Higgs bundles over non-compact affine Gauduchon manifolds
Zhenghan Shen, Chuanjing Zhang, Xi Zhang
In this paper, we use the affine Hermitian-Yang-Mills flow to prove a generalized Donaldson-Uhlenbeck-Yau theorem on flat Higgs bundles over a class of non-compact affine Gauduchon…
Analytically stable Higgs bundles on some non-Kähler manifolds
Chuanjing Zhang, Xi Zhang
In this paper, we study Higgs bundles on non-compact Hermitian manifolds. Under some assumptions for the underlying Hermitian manifolds which are not necessarily Kähler, we solve t…
A Liouville theorem on complete non-Kähler manifolds
Yuang Li, Chuanjing Zhang, Xi Zhang
In this paper, we prove a Liouville theorem for holomorphic functions on a class of complete Gauduchon manifolds. This generalizes a result of Yau for complete Kähler manifolds to…
Higgs bundles over non-compact Gauduchon manifolds
Chuanjing Zhang, Pan Zhang, Xi Zhang
In this paper, we prove a generalized Donaldson-Uhlenbeck-Yau theorem on Higgs bundles over a class of non-compact Gauduchon manifolds.
The limit of the Hermitian-Yang-Mills flow on reflexive sheaves
Jiayu Li, Chuanjing Zhang, Xi Zhang
In this paper, we study the asymptotic behavior of the Hermitian-Yang-Mills flow on a reflexive sheaf. We prove that the limiting reflexive sheaf is isomorphic to the double dual o…
A note on curvature estimate of the Hermitian-Yang-Mills flow
Jiayu Li, Chuanjing Zhang, Xi Zhang
In this paper, we study the curvature estimate of the Hermitian-Yang-Mills flow on holomorphic vector bundles. In one simple case, we show that the curvature of the evolved Hermiti…
The conical complex Monge-Ampère equations on Kähler manifolds
Jiawei Liu, Chuanjing Zhang
In this paper, by providing the uniform gradient estimates for a sequence of the approximating equations, we prove the existence, uniqueness and regularity of the conical parabolic…
Semi-stable Higgs sheaves and Bogomolov type inequality
Jiayu Li, Chuanjing Zhang, Xi Zhang
In this paper, we study semistable Higgs sheaves over compact Kähler manifolds, we prove that there is an approximate admissible Hermitian-Einstein structure on a semi-stable refle…