6 papers
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.