Poisson metrics and Higgs bundles over noncompact Kähler manifolds

Abstract

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-Simpson's nonabelian Hodge correspondence to noncompact Kähler manifolds setting.

29 pages

References in corpus (4)

• Asymptotic behaviour of tame harmonic bundles and an application to pure twistor $D$-modules
• Kobayashi-Hitchin correspondence for tame harmonic bundles and an application
• Projectively flat bundles and semi-stable Higgs bundles
• The limit of the harmonic flow on flat complex vector bundle