The limit of the harmonic flow on flat complex vector bundle

TL;DR

This paper investigates the asymptotic behavior of harmonic flow on flat complex vector bundles, establishing that the limit corresponds to the graded bundle derived from the Jordan-Hölder filtration.

Contribution

It proves that the harmonic flow's limit on flat complex vector bundles is isomorphic to the graded bundle from the Jordan-Hölder filtration, revealing a fundamental structural property.

Findings

Harmonic flow converges to a graded flat bundle

Limit is isomorphic to the Jordan-Hölder associated bundle

Provides a characterization of the flow's asymptotic behavior

Abstract

In this paper we study the limiting behaviour of the harmonic flow on flat complex vector bundle, and prove the limit must be isomorphic to the graded flat complex vector bundle associated to the Jordan-H\"older filtration.