本项目中我们将着重研究复向量丛上典则度量的存在性、相关热流的收敛性以及Yang-Mills-Higgs理论中的一些几何分析问题。首先在一类非紧Gauduchon流形上研究解析稳定或者半稳定希格斯丛上典则度量的存在性；在拟射影流形上研究半稳定抛物希格斯丛和全纯对上更为广泛的Hitchin-Kobayashi对应；研究非稳定希格斯层上的Hermitian-Yang-Mills-Higgs 热流的收敛性，建立其极限希格斯层与代数几何中的Harder-Narasimhan-Seshadri 滤过之间的对应关系，并刻画其blow-up集。

In this project, we study the existence of the canonical metrics on complex vector bundles, the convergence of the related heat flows and some geometric analysis problems in Yang-Mills-Higgs theory. First, we study the existence of the canonical metrics on analytic stable or semistable Higgs bundles over noncompact Gauduchon manifolds. Second, we study the generalized Hitchin-Kobayashi correspondence for semistable parabolic Higgs bundles and holomorphic pairs on quasiprojective manifolds. Then, we study the convergence of the Hermitian-Yang-Mills-Higgs flow on nonstable Higgs sheaves, construct the correspondence between the limiting Higgs sheaf and the Harder-Narasimhan-Seshadri filtration of the initial Higgs sheaf, and obtain the information of the blow up set.