4 papers · 1 filter
Liouville theorems for harmonic 1-forms on gradient Ricci solitons
Chenghong He, Di Wu, Xi Zhang
We prove that there is no nontrivial -integrable harmonic 1-form on noncompact complete gradient steady Ricci solitons or noncompact complete gradient shrinking Kähler-Ricci s…
Hermitian-Einstein equations on noncompact manifolds
Di Wu, Xi Zhang
This paper first investigates solvability of Hermitian-Einstein equation on a Hermitian holomorphic vector bundle on the complement of an arbitrary closed subset in a compact Hermi…
Prescribing Chern scalar curvatures on noncompact manifolds
Di Wu, Xi Zhang
In this paper, we investigate the noncompact prescribed Chern scalar curvature problem which reduces to solve a Kazdan-Warner type equation on noncompact non-Kähler manifolds. By i…
Harmonic metrics and semi-simpleness
Di Wu, Xi Zhang
Given a flat vector bundle over a compact Riemannian manifold, Corlette and Donaldson proved that it admits harmonic metrics if and only if it is semi-simple. In this paper, we ext…