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In this paper, we study the existence of Poisson metrics on flat vector bundles over noncompact Riemannian manifolds and discuss related consequence, specially on the applications in Higgs bundles, towards generalizing Corlette-Donaldson-Hitchin-Simpsons nonabelian Hodge correspondence to noncompact K{a}hler manifolds setting.
In this paper we survey the recent developments of the Ricci flows on complete noncompact K{a}hler manifolds and their applications in geometry.
We prove that a complete noncompact K{a}hler manifold $M^{n}$of positive bisectional curvature satisfying suitable growth conditions is biholomorphic to a pseudoconvex domain of {bf C}$^{n}$ and we show that the manifold is topologically {bf R}$^{2n}
In this note, we propose an approach to the study of the analogue for unipotent harmonic bundles of Schmids Nilpotent Orbit Theorem. Using this approach, we construct harmonic metrics on unipotent bundles over quasi-compact Kahler manifolds with care
We consider a version of Hermitian-Einstein equation but perturbed by a Higgs field with a solution called a Donaldson-Thomas instanton on compact Kahler threefolds. The equation could be thought of as a generalization of the Hitchin equation on Riem
We study the space of nearly K{a}hler structures on compact 6-dimensional manifolds. In particular, we prove that the space of infinitesimal deformations of a strictly nearly K{a}hler structure (with scalar curvature scal) modulo the group of diffeom