Poisson metrics and Higgs bundles over noncompact K\"{a}hler manifolds

TL;DR

This paper investigates Poisson metrics on flat vector bundles over noncompact Kähler manifolds and explores their implications for Higgs bundles, aiming to extend the nonabelian Hodge correspondence to noncompact settings.

Contribution

It introduces new conditions for the existence of Poisson metrics on noncompact Kähler manifolds and applies these results to generalize the nonabelian Hodge correspondence.

Findings

Established existence criteria for Poisson metrics on noncompact Kähler manifolds.

Extended nonabelian Hodge correspondence to noncompact Kähler manifolds.

Provided applications to Higgs bundle theory.

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 K\"{a}hler manifolds setting.